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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA265 - Numerical linear algebra  
 
Syllabus adopted 2016-02-15 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   24 Oct 2017 pm SB,  05 Jan 2018 am SB  

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPPAS PHYSICS AND ASTRONOMY, MSC PROGR, Year 2 (elective)
TKITE SOFTWARE ENGINEERING, Year 3 (elective)
TKITE SOFTWARE ENGINEERING, Year 2 (elective)

Examiner:

Professor  Larisa Beilina



  Go to Course Homepage

Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Basic knowledge of numerical analysis and linear algebra.

Aim

To give the students knowledge and skill in using algorithms and numerical software for linear algebra problems.

Learning outcomes (after completion of the course the student should be able to)

- use numerical linear algebra as building bricks in computation
- make a linear algebra model of a problem from the physical reallity
- derive and use the numerical tecniques needed for a professional solution of a given linear algebra problem
- use computer algorithms, programs and software packages to compute solutions to current problems
- critically analyze anf give advice regarding different choices of models, algorithms, and software with respect to efficience and reliability
- critically analyze the accuracy of the obtained numerical result and to present it in a visualized way.

Content

Numerical linear algebra problems arise in many different fields of science like solid mechanics, electrical networks, signal analysis and optimisation. In this course we study basic linear algebra concepts like matrix algebra, vector- and matrix norms, error analysis and condition numbers. For solving linear systems of equations we consider Gaussian elimination with different pivoting strategies. For least-squares problems we study QR-factorisation and singular value decomposition. The metods for eigenvalue problems are based on transformation techniques for symmetric and nonsymmetric matrices.
We discuss the numerical algorithms with respect to computing time and memory requirements. By homework assignments and project work the students get experiences in implementation and evaluation of numerical algorithms for linear algebra problems.

Organisation

Lectures, supervising of hand-ins and computer exercises

Literature

Numerical Linear Algebra: Theory and Applications, Larisa Beilina, Evgenii Karchevskii, and Mikhail Karchevskii, Springer 2016.

Examination

Experimental and homework assignments(hand-ins) and written examination.


Page manager Published: Thu 04 Feb 2021.