1. komponenta

Lecture type	Total
Lectures	15
Exercises	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The aim of the course is acquirement of skills for application of numerical methods by computer implementation. The emphasise is on better understanding the terms: approximation, perturbation, stability. Tutorials are organized as implementation of the methods in a programming language (C, FORTRAN, with controlled usage of available program libraries), with aim to introduce development of the methods to our students. By doing that, the skills for development of (libraries) mathematical software are developed, too.

COURSE DESCRIPTION AND SYLLABUS:
1. Definition of the environment (selection of a higher programming language and a mathematical software library (BLAS, LAPACK) for the implementation of algorithms). (2 weeks)
2. Iterative methods for solving linear systems. Independent implementation of one simple method. Practical usage of learned methods on study examples from application. The state of the art mathematical software libraries are applied. Implementation on a parallel computer (if available). (4 weeks)
3. Independent implementation of one (simple) method for diagonalization. Eigenvalue problems and SVD in applications - selected examples are solved by using the LAPACK library. (4 weeks)
4. Least squares method. Regularization. Numerical solution of integral equations in practice. (3 weeks)

1. J. Demmel: Applied Numerical Linear Algebra
2. R. Plato: Concise Numerical Mathematics
3. A. Greenbaum: Iterative methods for solving linear systems
4. B. Parlett: The symmetric eigenvalue problem
5. G. Golub, Ch. Van Loan: Matrix computations

Mandatory course - Regular study - Applied Mathematics