Numerical linear algebra
Code  Completion  Credits  Range  Language 

D01NLA_EN  ZK  2P  English 
 Garant předmětu:
 Ivana Pultarová
 Lecturer:
 Ivana Pultarová
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

Students are introduced to basic computational methods related to the problems of linear algebra which can be obtained in engineering problems. The following topics are studied. Basics of linear algebra: vectors, matrices, systems of linear equations, solvability. Vector and matrix norms, eigenvalues and eigenvectors. Spectra of matrices. Coordinates with respect to a basis; change of a basis. Schur complement. Symmetric and positive definite matrices. Gauss elimination. LU decomposition. Matrix iterative methods: Jacobi method, GaussSeidel method. Gradient methods: method of steepest descent, conjugate gradient method. Convergence criteria and convergence rate. Conditioning of a system of linear equation. Preconditioning methods. Incomplete LU decomposition. Eigenproblems. GramSchmidt orthogonalization. Discrete Fourier transformation and its properties. Circulent matrix.
 Requirements:

Participating at classes.
Completening homeworks and seminar works.
 Syllabus of lectures:

1. Vectors, matrices, systems of linear equations.
2. Norms, inner product.
3. Eigenvalues and eigenvectors. Conditioning.
4. Gauss elimination. Iterative methods.
5. Jacobi method. GaussSeidel method. Steepest descent method.
6. Conjugate gradient method.
7. Convergence.
8. Preconditioning.
9. Incomplete LU decomposition.
10. Discrete Fourier transform.
 Syllabus of tutorials:

1.2. Matlab or another solution software.
3. Arrays and matrices. Positive definite matrices.
4.6. Iterative methods.
7. Convergence
8.9. Preconditioning. Conjugate gradient method.
10. Matrix decomposition.
 Study Objective:

The goal is to improve students§ skill in numerical methods of linear algebra with applications in practical problems.
 Study materials:
 Note:
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: