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Course syllabus - Numerical Linear Algebra

Scope

7.5 credits

Course code

MAA517

Valid from

Autumn semester 2026

Education level

Second cycle

Progressive Specialisation

A1F (Second cycle, has second-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

Department of Business and Mathematics

Ratified

2019-12-09

Revised

2025-11-03

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2021-06-24
    • Latest update: 2025-05-27

    Books

    Demmel, James W.

    Applied Numerical Linear Algebra

    Språk: Engelska Antal sidor: 184 Upplaga: illustrated ed Förlag: Society for Industrial and Applied Mathematics ISBN: 9780898713893

    Other Materials

    Additional material in the form of Lecture notes might be provided during the course.

Objectives

The objective of the course is to give the student opportunity to acquire advanced knowledge of how large linear equation systems are used and managed in a numerical context.

Learning outcomes

Upon completion of the course, the student is expected to be able to

  1. discuss, in qualitative and quantitative terms, the advantages and disadvantages of different methods for operating on sparse matrices
  2. describe a few matrix decompositions and explain why they can be useful, and use numerical algorithms for computing a few common decompositions
  3. describe different algorithms for solving large linear equation systems and eigenvalue problems and discuss their properties with respect to convergence, stability, accuracy and efficiency
  4. use software for mathematical computations and determine if the results are reasonable

Course content

  • Direct and iterative methods for solving linear equation systems, e.g. Jacobi's method and the conjugate gradient method
    Properties of matrix operations related to stability, e.g. preconditioning and pivoting
  • Direct and iterative methods for solving eigenvalue problems, e.g. Power method and Krylov subspace methods
  • Decomposition of matrices, e.g. Cholesky, LU, QR and SVD
  • Discussion and examples of how large linear equation systems with different properties appear in numerical analysis, graph theory, statistics and data analysis

Specific requirements

Applied Matrix Analysis, 7.5 credits or other advanced course in Linear Algebra, and one course that has included either computer programming or usage of software for numerical computations. In addition, Swedish course 3 or Swedish level 3 and English course 6 or English level 2 are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3 or Swedish level 3.

Examination

INL1, Assignment, 4.5 credits, written assignments concerning learning outcomes 1-4, grades Fail (U) or Pass (G).
TEN1, Written examination, 3 credits, individual written examination concerning learning outcomes 1-3, grades Fail (U), 3, 4 or 5.

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3