Aktuel periode 2018 Spring
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MM843: Numerical Linear Algebra (5 ECTS)

STADS: 13016901

Level
Master's level 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 Comment
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
  • 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 
 


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:


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 or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.