Syllabus for |
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TMA891 - Large and sparse matrix problems
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| Syllabus adopted 2015-02-11 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: First-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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This course round is given every other year. Is given 2015/2016 but not 2016/2017
The course is cancelled
Teaching language: English
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0101 |
Examination |
7,5c |
Grading: TH |
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7,5c
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In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
Examiner:
Professor
Larisa Beilina
Go to Course Homepage
Eligibility:
In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.
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.
Learning outcomes (after completion of the course the student should be able to)
1. Understand the concept and characteristics of a large sparse problem
2. Understand and handle the most important methods used nowadays for solving large sparse linear systems and to compute eigenvalues for such problems.
3. To a certain extent derive, write computer programs for, and use the numerical techniques needed for a professional solution of a given large and sparse matrix problem
4. Use computer algorithms, programs and software packages to compute solutions to current problems
5. Critically analyze and give advice regarding different choices of models, algorithms, and software with respect to efficiency and reliability.
6. Critically analyze the accuracy of the obtained numerical result by performing error analysis and to present the result in a visualized way.
Content
Large and sparse matrix problems arise for instance in numerical approximation of differential equations, network problems and optimization. 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 (with and without preconditioning) 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.
Organisation
Lectures
Guidance in the solution of homework and experimental assignments
Literature
James W. Demmel: Applied Numerical Linear Algebra, SIAM 1997, chapters 6-7.
Lecture notes on direct methods for large sparse matrices.
Examination
Written examination, homework assignments, and computer exercises.