Numerical method of algebra

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Systems of linear equations. Direct methods: Gauss elimination and LU decomposition. Classical iterative methods: Jacobi and Gauss-Seidel. Successive over-relaxation. Steepest descent method and conjugate gradient method.

Modern and multilevel methods. Methods for eigenvalues and eigenvectors. Nonlinear equations.

Requirements:

Syllabus of lectures:

1. -2. Systems of linear equations. Eigenvalues and eigenvectors.

3.-4. Direct methods: Gauss elimination and LU decomposition

5.-6. Classical iterative methods.Jacobiho and Gauss-Seidel methods.

7.-8. Conjugate gradient methods.

9.-10. Modern methods.

11.-12. Methods for eigenvalues and eigenvectors.Systems of nonlinear equations.

Syllabus of tutorials:

1. -6. Application of direct and classical iterative methods in technical problems.

7.-12. Steepest descent method, conjugate gradient method. Modern and multilevel methods.

Study Objective:

Systems of linear equations. Direct methods: Gauss elimination and LU decomposition. Classical iterative methods: Jacobi and Gauss-Seidel. Successive over-relaxation. Steepest descent method and conjugate gradient method.

Modern and multilevel methods. Methods for eigenvalues and eigenvectors. Nonlinear equations.

Study materials:

[1] M.Fiedler: Speciální matice a jejich použití v numerické matematice, SNTL, Praha, 1981.

[2] K.Segeth: Numerický software I.,Karolinum, Praha 1998.

[3] A.George, J.W.Liu: Computer Solution of Large Sparse Positive Definite Systems, NY,1981.

[4] G.H.Golub, Ch.F.van Loan: Matrix Computations, Johns Hopkins Univ. Press, Baltimore, 1996.

[5] G. Meurant: Computer Solution of Large Linear Systems, Elsevier, Amsterdam, 1999.

[6] C.T. Kelley: Solving Nonlinear Equations with Newton's Method, SIAM, Philadelphia, 2003.

[7] E. Vitásek, Numerické metody, 1987, TP

[8] P. Sváček, M. Feistauer, Metoda konečných prvků,skripta str. 67-76,Vydavatelství ČVUT

[9] Y. Saad, Iterative methods for sparse linear systems, 2007, IAM

http://www-users.cs.umn.edu/~saad/books.html

kapitoly 1 (str. 1-41), kapitoly 3.1-3.2, 3.4, a kapitolu 4

Note:

Further information:

http://marian.fsik.cvut.cz/~svacek/numalg/index.html

No time-table has been prepared for this course

The course is a part of the following study plans: