COURSE AIMS AND OBJECTIVES:
To study iterative methods for solving of systems of linear equations, the matrix problem of eigenvalues, and boundary problems for ordinary differential equations.
COURSE DESCRIPTION AND SYLLABUS:
1. Iterative methods for solving of linear systems. Introduction. Classical methods: Jacobi, Gauss - Seidel, SQR method. General iterative method. Convergence. Error estimates. Sufficient conditions for convergence - classical methods. Symetrical matrices.
2. Eigenvalues and singular values for matrices. Basic results. Absolute and relative estimates
3. Calculating spectral decomposition of symmetrical matrices. Jacobi method. Reduction of symmetric matrix to three diagonal form. QR alghoritm. Other methods.
4. Methods for solving ordinary differential equations. Euler method, Cauchy problem, RK methods, method of finite differences.
MATLAB will be used during the course.