MM843: Numerical Linear Algebra

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310036102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310036101
ECTS value: 5

Date of Approval: 01-11-2022


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with MM559.

Entry requirements

None

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of the contents of MM536
  • Have knowledge of the contents of MM540, MM505 or MM568
  • 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
  • compare and contrast the methods introduced in the course
  • understand the quantitative and qualitative aspects of numerical convergence of the methods
  • transfer the learning content to new problems
  • create and customize algorithms for related applications
  • reflect the overarching pattern 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) and Minimum residual method (MINRES) and generalized minimum residual method (GMRES)
  • Error analysis

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring and June

Tests

Mandatory assignments, oral exam

EKA

N310036102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

42 hours per semester

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

Teacher responsible

Name E-mail Department
Ralf Zimmermann zimmermann@imada.sdu.dk Computational Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.