Course syllabus - Numerical Linear Algebra

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 B/Swedish 3 and English A/English 6 are required. In cases when the course is offered in English, the requirement for Swedish B/Swedish 3 is excluded.

Examination

INL1, Written 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 a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3