Numerical methods of algebra

Garant předmětu:

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Department of Technical Mathematics

Synopsis:

Elementary problems of linear algebra and their formulation.

Direct methods of solution of systém of linear equations.

Classical iterative methods, Jacobi, Gauss-Seidel and super-relaxation methods.

Gradient methods, steepest descent and conjugate gradient methods.

GMRES method.

Ill conditioned problems and their solution, pre-conditioning.

Solution of eigenvalue problems, generalized eigenvalue problems.

Solution of systems of non-linear aglebraic equations.

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Study materials:

C.T. Kelley , Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995

M. Fiedler.: Speciální matice a jejich použití v numerické matematice, SNTL, 1981.

R.S. Varga, Matrix Iterative Analysis, Springer 2009.

A.George, J.W Liu.: Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall 1981.

Golub, G.H., van Loan, Ch.F.: Matrix Computations, 996 The Johns Hopkins Univ. Press.

Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations, 1994, Springer-Verlag

Meurant, G.: Computer Solution of Large Linear Systems, 1999, Elsevier.

Segeth, K.: Numerický software I., 1998, Karolinum.

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: