F5330 Basic numerical methods

Faculty of Science
Autumn 2010 - only for the accreditation
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.
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.
The course is taught: every week.
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 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, 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.