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Course, academic year 2023/2024
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Sparse Matrices in Numerical Mathematics - NMNV533
Title: Řídké matice v numerické matematice
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
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
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.
Aim of the course -
Last update: prof. Ing. Miroslav Tůma, CSc. (08.10.2017)

To understand basic ideas related to sparse matrices in direct methods as well as approximate factorizations

used as preconditioners in iterative methods.

Course completion requirements -
Last update: prof. Ing. Miroslav Tůma, CSc. (25.09.2020)

Needed to get credits:

• students will independently prepare one or two presentations for the other students

based on the agreement with the lecturer

It necessary, everything will be distant.

Literature -
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, J. Reid. Direct methods for Sparse Matrices, Clarenton Press, Oxford University Press, 1986.

J. Dongarra, I.S. Duff, D. Sorensen, 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.

Teaching methods -
Last update: prof. Ing. Miroslav Tůma, CSc. (25.09.2020)

Lectures and tutorials in a distant way.

Requirements to the exam -
Last update: prof. Ing. Miroslav Tůma, CSc. (25.09.2020)

Examination according to the syllabus. Posssibly distant.

• students will be asked one thematically general question

• students will have enough time to prepare their answer

• they should show basic understanding to parallel matrix computations

• examining persons can pose subquestions related to the main question

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

1. Basic terminology from computers, factorizzations and computational complexity.

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

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

algorithmic synthesis of sparse direct solvers.

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

Sparse QR decomposition. Sparse decompositions of symmetric indefinite systems.

5. Implementations of direct and approximate solvers.

The exam will test basic understanding to the subject described in this sylabus.

The exam can preceed getting credits. The credits will be given based on the student activity.

In order to ge the credits, at least one talk based on an independent work offered by the lecturer should

be given.

Entry requirements -
Last update: prof. Ing. Miroslav Tůma, CSc. (16.05.2018)

Premiliminary for this course is only a basic knowledge of linear algebra that corresponds, for example, to NMAG101.

Some knowledge of basic graph theory is an advantage but not a necessity.

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