F5330 Basic numerical methods

Faculty of Science
Autumn 2010
Extent and Intensity
1/1/0. 3 credit(s). Type of Completion: z (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: doc. RNDr. Jan Celý, CSc.
Timetable
Wed 17:00–17:50 F1 6/1014, Wed 18:00–18:50 F1 6/1014
Prerequisites
Knowledge of the programming (Pascal,Fortran, C,C++)
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 course presents to students knowledge on basic numerical methods: matrix operations, solving systems of linear algebraic equations and regression. Another part of the lecture deals with polynomial interpolation and solution of one-dimensional nonlinear equations.

After successful passing of the course the students should be able to
- list and describe basic numerical methods lectured
- successfully apply these methods for solving a specified problem.
Syllabus
  • 1) Number representation in a computer,precision, accuracy. Errors in numerical algorithms, propagation of the errors. Stability of the algorthims. Ill-posed methods.
  • 2) Systems of linear algebraic equations, direct and iterative metods.
  • The Gauss elimination method, pivoting. LU decomposition.
  • Systems with special matrices: The Choleski theorem and the Choleski method, tridiagonal systems.
  • Iterative methods: the Jacobi method, the Gauss-Seidel method. The problem of the convergence of the iteration methods.
  • 3) Eigenvalues and eigenvectors of matrices. The Jacobi-method. The Householder transformation and the QR algorithm.
  • Iterative methods: the power method, convergence.
  • 4) Singular value decomposition and its applications. Linear regression.
  • 5) Interpolation: divided difference tables, polynomial interpolation, cubic splines.
  • 6) The solution of nonlinear equations in 1D: bisection, Newton's and secant method, fixed-point iteration.
Literature
  • MÍKA, Stanislav. Numerické metody algebry. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1982, 169 s. info
  • HUMLÍČEK, Josef. Základní metody numerické matematiky. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1981, 171 s. info
  • CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985, 99 s. info
  • PRESS, William H. Numerical recipes in C : the art of scientific computing. 2nd ed. Cambridge: Cambridge University Press, 1992, xxvi, 994. ISBN 0521431085. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
  • CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
  • PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. info
Teaching methods
Lecture + individual work on PC.
Assessment methods
Requirements for credit: knowledge on topics presented in the lectures + discussion of worked out programs.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~jancely
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2010, recent)
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