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The course is devoted to the most widely used iterative methods for solving systems of linear algebraic equations, linear approximation problems, eigenvalue problems, etc., including preconditioning.
The emphasis is put especially on effective algorithmic realization and study of convergence properties.
Last update: Kučera Václav, doc. RNDr., Ph.D. (05.12.2018)
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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: Hnětynková Iveta, doc. RNDr., Ph.D. (07.09.2020)
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Saad, Y.: Iterative methods for sparse linear systems, SIAM, Philadelphia, 2003 (2nd ed.).
Liesen, J., Strakos, Z.: Krylov Subspace Methods, Oxford University Press, 2012.
Barrert, R., et all: Templates for the solution of linear systems: Building blocks for iterative methods, SIAM, Philadelphia, 1994.
Higham, N.: Accuracy and stability of numerical algorithms, SIAM, Philadelphia, 2002 (2nd ed.).
Meurant, G.: Computer solution of large linear systems, Studies in Mathematics and Its Applications, North-Holland, 1999.
http://karlin.mff.cuni.cz/~pozza/ Last update: Pozza Stefano, Dr., Ph.D. (07.09.2020)
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Lectures are held in a lecture hall, practicals in a computer laboratory (Matlab enviroment). In case of distance learning, online communication platforms will be used (e.g. MOODLE, ZOOM). Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (07.09.2020)
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The exam reflects all the material presented in lectures and practicals during the whole semester. Critical thinking and data literacy, in the form of understanding the connection between data and methods, are also expected learning outcomes of the course. The exam has oral form.
When needed, it is possible to take the exams or credits in a distance form. Last update: Pozza Stefano, Dr., Ph.D. (14.07.2021)
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1. Idea and basic principles of iterative methods. Introduction to work with sparse and structured matrices.
2. Methods for solving systems with symmetric matrices.
3. Methods for solving systems with nonsymmetric matrices based on orthogonality and long recurrences, and based on biorthogonality and short recurrences.
4. Methods for solving linear approximation and ill-posed problems.
5. Generalizations for problems with multiple observations - block and band methods.
6. Preconditioning - idea, selection, construction.
7. Convergence and numerical stability - comparison and examples.
8. Multigrid - idea. Last update: Pozza Stefano, Dr., Ph.D. (07.09.2020)
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Previous knowledge of linear algebra and basic methods for matrix computations is expected. Last update: Hnětynková Iveta, doc. RNDr., Ph.D. (07.09.2020)
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