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The course will deal with the general theory of projective methods, in particular, Krylov subspace methods and
their relation to the problem of moments.
Last update: T_KNM (27.04.2015)
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The course aims at understanding of matrix iterative methods for solving large linear algebraic problems, namely systems of linear algebraic equations. It will focus on mathematical fundamentals rather than on surveying methods and algorithms, and on addressing the question ``why'' rather than on an overwhelming information on ``how''. Last update: T_KNM (12.09.2013)
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The exam has only oral part. Questions reflect the syllabus within the scope covered in the lectures. Emphasize is given to understanding the principles, the motivation and rigorous interpretation of the developed results, as well as to the interconnections between different views and approaches.
Zkouška má pouze ústní část. Otázky vycházejí ze sylabu ve rozsahu odpřednášené látky. Důraz je kladen na porozumění principům, motivaci a přesnou interpretaci odvozených výsledků, stejně jako na souvislosti mezi různými pohledy a přístupy. Last update: Strakoš Zdeněk, prof. Ing., DrSc. (08.06.2019)
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J. Liesen and Z. Strakos, Krylov Subspace Methods, Principles and Analysis, Oxford University Press, 2012, 408p;
W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, 1994, 429p.;
Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM Publications, 2003, 528p.;
Y. V. Vorobyev, Method of Moments in Applied Mathematics, Gordon and Breach Sci. Publ., 1965, 165p. Last update: T_KNM (12.09.2013)
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The exam has only oral part. Questions reflect the syllabus within the scope covered in the lectures. Emphasize is given to understanding the principles, the motivation and rigorous interpretation of the developed results, as well as to the interconnections between different views and approaches. Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
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The course will cover primarily projection methods and, in particular, Krylov subspace methods in relation to the problem of moments and related issues. The emphasis will be on interconnections between the relevant topics from various disciplines, including the elements of numerical solution of partial differential equations, approximation theory and functional analysis.
Tentative content:
1. Projection processes 2. Krylov subspaces 3. Basic methods 4. Stieltjes moment problem 5. Orthogonal polynomials, continued fractions, Gauss-Christoffel quadrature and model reduction 6. Matrix representation and the method of conjugate gradients 7. Vorobyev method of moments and non-symmetric generalizations 8. Non-normality and spectral information Last update: T_KNM (12.09.2013)
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The course assumes knowledge corresponding to the course NMNM331 Analysis of Matrix Computations 1, which uses the textbook J. Duintjer Tebbens, I.Hnetynkova, M. Plesinger, Z. Strakos and P. Tichy, Analysis of methods for matrix computations, Basic methods (in Czech), Matfyzpress Prague, ISBN 978-80-7378-201-6, 2012, 328 p. The knowledge corresponding to the content of the course NMNM332 Analysis of Matrix Computations 2 is recommended, but not a strict prerequisite. Last update: T_KNM (16.09.2013)
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