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MM559: Numerical Linear Algebra (5 ECTS)

STADS: 13017001

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible

Email: zimmermann@imada.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Monday	09-11	IMADA semi	6
Common	I	Tuesday	14-16	U66	6,8-12
Common	I	Wednesday	10-12	IMADA semi	8-12,14
Common	I	Thursday	10-12	IMADA semi	8-12,15
Common	I	Thursday	10-12	U152	14
Common	I	Friday	10-12	U151	14
H1	TE	Wednesday	10-12	IMADA semi	8-12,14
H1	TE	Thursday	10-12	IMADA semi	15

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Comment:
Ubegrænset deltagerantal

Prerequisites:
None

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

Subject overview

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

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

Mandatory assignments, oral exam. Internal marking, 7-mark scale. (5 ECTS). (13017002).

A closer description of the exam rules will be posted under 'Course Information' on Blackboard.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
- Tutorials: 14 hours

Educational activities

Reading of suggested literature
Preparation of exercises in study groups
Contributing to online learning activities related to the course

Educational form
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.

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.