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### Iterative methods

 Code: 36920 ECTS: 5.0 Lecturers in charge: izv. prof. dr. sc. Zvonimir Bujanović - Lectures Lecturers: izv. prof. dr. sc. Zvonimir Bujanović - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
Description:
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.
Literature:
1. L. N. Trefethen, D. Bau: Numerical Linear Algebra
2. E. Suli, D. Mayers: Introduction to Numerical Analysis
3. G. H. Golub, C. F. van Loan: Matrix Computations, 2nd edition
4. K. E. Atkinson: An introduction to numerical analysis, 2nd edition
Prerequisit for:
Enrollment :
Passed : Numerical mathematics
 5. semester Izborni predmet 1, 2 - Regular study - Mathematics 6. semester Izborni predmet 1, 2 - Regular study - Mathematics
Consultations schedule:
• izv. prof. dr. sc. Zvonimir Bujanović: