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Course, academic year 2023/2024
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Matrix Iterative Methods 2 - NMNV438
Title: Maticové iterační metody 2
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Iveta Hnětynková, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Interchangeability : NMNV411
Annotation -
The course is devoted to the most widely used Krylov subspace iterative methods for solving systems of linear algebraic equations, linear approximation problems and eigenvalue problems. The emphasis is put especially on effective algorithmic realization and convergence analysis. The course extends some topics discussed in the course Analysis of Matrix Calculations 1 (NMNM331).
Last update: T_KNM (07.04.2015)
Course completion requirements -

To finish the course successfully, it is required to pass the exam covering all presented topics, see "Requirements to the exam".

Furthermore, students will complete one homework assignments during the semester. The homework consists of implementing a selected method in the MATLAB environment.

Last update: Pozza Stefano, Dr., Ph.D. (23.04.2020)
Literature -

Saad, Y.: Iterative methods for sparse linear systems, SIAM, Philadelphia, 2003.

Liesen, J., Strakos, Z.: Krylov Subspace Methods, Principles and Analysis, Oxford University Press, 2012.

Barrert, R., et all: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994.

Meurant, G.: Computer solution of large linear systems, Studies in Mathematics and Its Applications, North-Holland, 1999.

Freund, R., Nachtigal, N.: QMR: A quasi-minimal residual method for non-hermitian linear systems. Numer. Math. 60, pp. 315-339, 1991.

Saad, Y., Schultz, M.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7, pp. 856-869, 1986.

Paige, C., Saunders, M.: LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software 8, pp. 43-71, 1982.

Paige, C., Saunders, M.: Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal. 12, pp. 617-629, 1975.

More information:

Last update: Pozza Stefano, Dr., Ph.D. (10.02.2020)
Teaching methods -

Lectures are held in a lecture hall, practicals in a computer laboratory (Matlab enviroment).

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (07.04.2015)
Requirements to the exam -

The exam reflects all the material presented on lectures and practicals during the whole semester. The exam has oral form.

It is probable that a large part of the exams or credits could take place in a distance form. It depends on a development of the situation and we will inform you about the changes immediately.

Last update: Pozza Stefano, Dr., Ph.D. (23.04.2020)
Syllabus -

1. Methods for solving symmetric linear systems of equations - Lanczos method, SYMMLQ, MINRES.

2. Methods for solving nonsymmetric linear systems of equations based on orthogonality and long recurrences - FOM, GMRES.

3. Methods for solving nonsymmetric linear systems of equations based on biorthogonality and short recurrences - CGS, BiCG, BiCGstab, QMR, TFQMR.

4. Methods connected with normal equations - CGLS, LSQR.

5. Block methods.

6. Idea of preconditioning.

7. Convergence and numerical stability - comparison and examples.

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (01.02.2016)
Entry requirements -

Previous knowledge of linear algebra and basic methods for matrix computations is expected.

Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (30.04.2018)
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