MM559: Numerical Linear Algebra
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300043102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300043101
ECTS value: 5
Date of Approval: 27-10-2018
Duration: 1 semester
Version: Archive
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to:
- Have knowledge of the contents of MM536
- Have knowledge of the contents of MM540 or MM505
- Have knowledge of the contents of MM533
Course introduction
The aim of the course is to obtain knowledge about iterative solution techniques for linear equation systems. The student is enabled:
- to analyse, apply and modify these techniques by means of mathematical and numerical analysis
- to formulate the problems (including proofs) in a correct mathematical language
- to implement algorithms as computer programs and compute numerical approximations to large and sparse linear equation systems
The course builds on the knowledge acquired in the courses MM536: Calculus for mathematics, MM505: Linear Algebra or MM540: Mathematical methods for economics, MM533 Mathematical and numerical analysis.
The course has connections to MM546: Partial differential equations: theory, modelling and simulation and gives an academic basis for further studies in applied mathematics in general and in particular for Bachelor and Master thesis topics.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to analyse the qualitative and quantitative characteristics of a mathematical model
- Give basic understanding on how to perform computer based calculations in science, technology and economy
- Give knowledge and understanding of basic algorithms
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- understand the basic principles of iterative solution methods
- understand and work with matrix norms, sparse matrices, subspaces, projections
- understand the quantitative and qualitative aspects of numerical convergence of the methods
Content
The following main topics are contained in the course:
- Vector and matrix norms
- Sparse matrices
- Subspaces and projections
- Canonical forms of matrices
- Perturbation and sensitivity results
- Iterative solution methods, including
- Orthomin and steepest descent
- Conjugate gradients (CG)
- Minimum residual method (MINRES) and generalized minimum residual method (GMRES)
- Error analysis
Literature
Examination regulations
Exam element a)
Timing
Spring and June
Tests
Mandatory assignments, oral exam
EKA
N300043102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
5
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
- Tutorials: 14 hours
Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.
Educational activities
- Reading of suggested literature
- Preparation of exercises in study groups
- Contributing to online learning activities related to the course