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Sparse Matrices in Direct Methods - NMNV533

Title:	Řídké matice v přímých metodách
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2016
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. Ing. Miroslav Tůma, CSc.
Class:	M Mgr. MMIB > Povinně volitelné M Mgr. NVM M Mgr. NVM > Povinně volitelné
Classification:	Mathematics > Numerical Analysis

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Annotation -

Last update: doc. RNDr. Václav Kučera, Ph.D. (15.01.2019)

The goal of this course is to present contemporary algorithms and techniques dealing with sparse matrices for solving large and sparse systems of linear equations. Such systems arise in many practical problems of mathematical modeling, for example as a result of discretizations of partial differential equations as well as in applications in such diverse fields as management science, economy or chemical and biological sciences.

Literature - Czech

Last update: doc. RNDr. Václav Kučera, Ph.D. (15.01.2019)

T. Davis. Direct Methods for Sparse Linear Systems. Fundamentals of Algorithms, 2. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2006.

G. Meurant. Computer Solution of Large Linear Systems. Studies in Mathematics and its Applications, 28. North-Holland Publishing Co., Amsterdam, 1999.

I.S. Duff, A. Erisman and J. Reid. Direct methods for Sparse Matrices, Clarenton Press, Oxford University Press, 1986.

J. Dongarra, I.S. Duff, D. Sorensen and H. A. van der Vorst. Solving Linear Systems on Vector and Shared Memory Computers, SIAM, 1991.

A.George, J. Liu: Computer Solution of Sparse Positive Definite Systems, Prentice-Hall, 1981.

J. Liu: The role of elimination trees in sparse factorization, SIAM. J. Matrix Anal. Appl. 11 (1990), 134-172.

Syllabus -

Last update: prof. Ing. Miroslav Tůma, CSc. (03.10.2017)

1. Direct methods, their representation by graphs and sparse matrices in applications.

2. Graph interpretation of Cholesky factorization and LU decomposition. Theoretical basis and

algorithmic synthesis of sparse direct solvers.

3. Direct and approximate methods. The use of approximate decompositions in preconditioning.

Sparse QR decomposition. Sparse decompositions of symmetric indefinite systems.

4. Implementations of direct and approximate solvers.