Course syllabus for Numerical linear algebra

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameNumerisk linjär algebra
  • CodeTMA265
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20138
  • Open for exchange studentsYes

Credit distribution

0101 Examination 7.5 c
Grading: TH		7.5 c
  • 25 Okt 2022 pm J
  • 05 Jan 2023 pm J
  • Contact examiner

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

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 including compulsory elements

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

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

The course syllabus contains changes

  • Changes to examination:
    • 2023-03-20: Exam date Exam date Exam by department added by Elisabeth Eriksson
      [36258, 58164, 3], New exam for academic_year 2022/2023, ordinal 3 (not discontinued course)
    • 2022-08-25: Exam date Exam date changed by Elisabeth Eriksson
      [36258, 58164, 2], New exam for academic_year 2022/2023, ordinal 2 (not discontinued course)