Numerical method of algebra
Code | Completion | Credits | Range |
---|---|---|---|
W01A004 | ZK | 45B |
- 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:
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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:
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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:
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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:
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[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: