F6150 Advanced numerical methods

Faculty of Science
Spring 2024
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 8:00–9:50 F1 6/1014
  • Timetable of Seminar Groups:
F6150/01: Mon 19. 2. to Sun 26. 5. Tue 10:00–10:50 F1 6/1014
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2025
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

F6150 Advanced numerical methods

Faculty of Science
Spring 2023
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Tue 10:00–11:50 Fcom,01034
  • Timetable of Seminar Groups:
F6150/01: Tue 12:00–12:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2022
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 14:00–15:50 Fcom,01034, Mon 16:00–16:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2021
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Tue 8:00–9:50 online_F3
  • Timetable of Seminar Groups:
F6150/01: Mon 1. 3. to Fri 14. 5. Tue 10:00–10:50 online_F3
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for colloquium: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2020
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 12:00–13:50 Fcom,01034
  • Timetable of Seminar Groups:
F6150/01: Mon 14:00–14:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
An introduction of advanced numerical methods, with a particular emphasis on spectral analysis and multidimensional optimalization. An emphasis is put on the applications of these methods when solving physical problems.
Learning outcomes
The main objective of the course is to provide the students with the ability to:
- list and explain the details of the lectured numerical methods;
- apply these methods in particular modelling tasks;
- learn to utilize suitable software to perform numerical simulations of physical systems.
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2019
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Tue 13:00–14:50 Fcom,01034
  • Timetable of Seminar Groups:
F6150/01: Mon 18. 2. to Fri 17. 5. Tue 15:00–15:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
spring 2018
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 13:00–14:50 Fcom,01034, Mon 15:00–15:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2017
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Wed 17:00–18:50 Fcom,01034, Wed 19:00–19:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2016
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 16:00–17:50 Fcom,01034, Mon 18:00–18:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2015
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 15:00–16:50 Fcom,01034, Mon 17:00–17:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2014
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Tue 16:00–17:50 Fcom,01034, Tue 18:00–18:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2013
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Tue 7:00–8:50 Fs1 6/1017, Wed 15:00–15:50 Fcom,01034
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Discrete Fourier transform (FFT algorithm, DFT of real data, DFT variants with symmetry - cosine and sine transforms, multidimensional DFT, applications: spectral analysis, filtering, convolution and deconvolution, jpeg and mp3)
  • 2. Multidimensional minimization (simplex method, Powell's method, conjugate-gradient methods, variable metric method, Marquardt-Levenberg algorithm for the sum of squares, simulated annealing, particle swarm method)
  • 3. Lanczos diagonalization of sparse matrices
  • 4. Numerical quadrature (Gaussian quadrature, Gauss-Kronrod rules, adaptive quadrature)
  • 5. Interpolation and approximation (polynomial interpolation - classical formulas and Neville's algorithm, cubic splines, rational interpolation, multidimensional case)
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: successful presentation of the solution of the assigned semestral project.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~chaloupka/F6150/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2012
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Tue 15:00–16:50 Fs1 6/1017, Thu 13:00–13:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: oral examination of topics knowledge on lectured topics + presentation of sufficient results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2011
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Thu 14:00–15:50 Fs1 6/1017, Thu 16:00–16:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: oral examination of topics knowledge on lectured topics + presentation of sufficient results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2010
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Wed 16:00–17:50 Kontaktujte učitele, Wed 18:00–18:50 Kontaktujte učitele
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: oral examination of topics knowledge on lectured topics + presentation of sufficient results of individual work during the semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Thu 15:00–16:50 Fs1 6/1017, Thu 17:00–17:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
During the semester students obtain basic knowledge on themes: Interpolation and aproximation, numerical quadrature,multidimensional minimization and nonlinear regression, initial-value and boundary-value problems for ODEs,introduction to solving PDEs, fast Fourier transform.
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Assessment methods
Lecture + individual work on PC. Demands for graded credit: have a good knowledge of topics presented in the lecture together with solid results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Tue 14:00–15:50 Fcom,01034, Thu 10:00–10:50 Kontaktujte učitele
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2007
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Fri 11:00–12:50 Fs1 6/1017, Fri 13:00–13:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2006
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Fri 10:00–11:50 Fs1 6/1017, Fri 12:00–12:50 Fs1 6/1017
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2005
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Timetable
Thu 14:00–15:50 F23-204, Thu 16:00–16:50 F23-204
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2004
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2003
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2002
Extent and Intensity
2/1/0. 3 credit(s). Type of Completion: graded credit.
Teacher(s)
prof. RNDr. Josef Humlíček, CSc. (lecturer)
prof. RNDr. Josef Humlíček, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2001
Extent and Intensity
2/1/0. 3 credit(s). Type of Completion: graded credit.
Teacher(s)
prof. RNDr. Josef Humlíček, CSc. (lecturer)
prof. RNDr. Josef Humlíček, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2000
Extent and Intensity
2/1/0. 3 credit(s). Type of Completion: graded credit.
Teacher(s)
prof. RNDr. Josef Humlíček, CSc. (lecturer)
prof. RNDr. Josef Humlíček, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus
  • 1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: oral examination of topics knowledge on lectured topics + presentation of sufficient results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to provide the students with the ability to
- list and describe the lectured numerical methods
- apply these methods in particular modelling tasks
Syllabus
  • 1. Polynomial interpolation and aproximation.
  • 2. Cubic interpolation spline.
  • 3. Data smoothing,smoothing spline.
  • 4. Numerical differentiation.
  • 5. Numerical quadrature: Newton-Cotes methods, Richardson extrapolation and Romberg quadrature, Gauss methods.
  • 6. Minimization of functions.
  • 7. Multidimensional optimization, nonlinear regression.
  • 8. Initial-value problem for ordinary differential equations: Runge-Kutta methods, multistep methods. 9. Boundary-value problem for ordinary differential equations. 10. Introduction to numerical solution of partial differential equations: heat equation in 1D, Laplace problem in 2D.
  • 11. Discrete Fourier transform, fast Fourier transform.
Literature
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • GIORDANO, Nicholas J. and Hisao NAKANISHI. Computational physics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1997, xiii, 544. ISBN 0131469908. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • GOULD, Harvey, Jan TOBOCHNIK and Wolfgang CHRISTIAN. An introduction to computer simulation methods : applications to physical systems. 3rd ed. San Francisco: Pearson Addison Wesley, 2007, xviii, 796. ISBN 0805377581. info
  • KOONIN, Steven E. and Dawn C. MEREDITH. Computational physics : Fortran version. Boulder, Colo.: Westview Press, 1990, 16, 639. ISBN 0201386232. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Demands for graded credit: oral examination of topics knowledge on lectured topics + presentation of sufficient results of individual work during the semester.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://monoceros.physics.muni.cz/~jancely
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F6150 Advanced numerical methods

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Josef Humlíček, CSc.
Prerequisites (in Czech)
F5330 Basic numerical methods
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
1. Interpolation. Polynomials. 2. Cubic interpolation spline. 3. Smoothing. Polynomials. 4. Trigonometric polynomials. Discrete Fourier transform. 5. Fast Fourier transform. 6. Numerical differentiation. 7. Numerical quadrature. 8. Romberg and Gauss quadrature. 9. Minimization of functions. 10. Multidimensional minimization. 11. Solving ordinary differential equations. 12. Solving partial differential equations.
Syllabus (in Czech)
  • 1. Interpolace funkcí. Polynomy. 2. Kubický interpolační splajn. 3. Vyhlazování. Polynomy. 4. Trigonometrické polynomy. Diskrétní Fourierova transformace. 5. Rychlá Fourierova transformace. 6. Numerické derivování. 7. Numerická intergrace. 8. Rombergova a Gaussova kvasratura. 9. Řešení transcendentních rovnic. 10. Minimalizace funkcí jedné proměnné. 11. Vícerozměrná minimalizace. 12. Řešení obyčejných diferenciálních rovnic. 13. Řešení parciálních diferenciálních rovnic.
Literature
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
  • ATKINSON, Kendall E. Elementary numerical analysis. 2nd ed. New York: John Wiley & Sons, 1993, xiii, 425. ISBN 0471600105. info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1985, 187 s. URL info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)