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Course, academic year 2017/2018
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Matrix Iterative Methods 1 - NMNV407
Czech title: Maticové iterační metody 1
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:4/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: prof. Ing. Zdeněk Strakoš, DrSc.
Class: M Mgr. MOD
M Mgr. MOD > Povinné
M Mgr. NVM
M Mgr. NVM > Povinné
Classification: Mathematics > Numerical Analysis
Incompatibility : NNUM130
Annotation -
Last update: T_KNM (27.04.2015)

The course will deal with the general theory of projective methods, in particular, Krylov subspace methods and their relation to the problem of moments.
Aim of the course
Last update: T_KNM (12.09.2013)

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)

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.

Requirements to the exam
Last update: prof. Ing. Zdeněk Strakoš, DrSc. (10.10.2017)

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.

Syllabus -
Last update: T_KNM (12.09.2013)

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

Entry requirements
Last update: T_KNM (16.09.2013)

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.

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