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## Syllabus for

TMA891 - Large and sparse matrix problems

Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: English

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 No Sp 0101 Examination 5,0 c Grading: TH 5,0 c Contact examiner

#### In programs

EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TM Teknisk matematik, Year 2 (elective)

#### Examiner:

Docent  Gunhild Lindskog

#### Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

#### Course specific prerequisites

Thorough knowledge of numerical linear algebra.

#### Aim

To give the students knowledge and skill in using algorithms and numerical software for large and sparse matrix problems.

#### Content

Large and sparse matrix problems arise for instance in numerical approximation of differential equations, network problems and optimisation. In this course we study numerical techniques for solution of systems of linear equations, eigenvalue problems and least-square problems with this type of matrices.
For systems of linear equations we present two classes of methods: iterative and direct. Among the iterative methods we study basic stationary methods like Jacobi and SOR methods, orthogonalising methods like conjugate gradients and multigrid methods. The direct methods are based on Gaussian elimination with different renumberings of the unknowns in order to keep computing time and memory requirement small.
For least-squares problems we consider sparse QR-factorisation and iterative orthogonalising methods.
The eigenvalue routines presented are based on Lanczos and Arnoldi algorithms with or without spectral transformations.
When solving the homework assignments and computer exercises, the students get experiences in implementation and evaluation of different algorithms for sparse problems.

#### Literature

Applied Numerical Linear Algebra, James W. Demmel, SIAM 1997, chapter 6-7
Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. van der Vorst, editors,
Templates for the solution of Algebraic Eigenvalue Problems: A Practical Guide .

#### Examination

Experimental assignments and oral presentation.

Page manager Published: Thu 03 Nov 2022.