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Iterative Methods for Linear Systems of Equations Martin van Gijzen

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DTU Informatics. Graduate School ITMAN.

Iterative Methods for Linear Systems of Equations

Martin van Gijzen

Delft University of Technology, The Netherlands

October 20 – 24, 2008

Department of Informatics and Mathematical Modelling, DTU, Denmark

Course description

The PhD course gives an overview of modern iterative methods for solving large systems of linear equations. Such systems arise in a variety

of applications such as image processing, optimization, data mining, medical and geophysical tomography, geodesy and oceanography.

The purpose of this course is to present state-of-the-art methods for such systems, with emphasis on a combination of practical computational

aspects and insight into the underlying theory for the methods.

Course requirements

The participants must have a fundamental knowledge of numerical analysis and linear algebra and must be able to program in Matlab. Students

are expected to read the course material before participating in the course.

Day 1 Introduction to iterative methods

Simple iterative methods (Jacobi, Gauss Seidel, SOR), simple iterative methods for the normal

equations (ART, SIRT) and one-dimensional projection methods.

Day 2 Projection methods (1)

Lanczos-based methods for symmetric systems: CG and MINRES. Methods for the normal

equations. Convergence theory.

Day 3 Projection Methods (2)

Arnoldi-based methods: GMRES and FOM. Convergence theory. Restarted GMRES, GMRESR.

Day 4 Projection Methods (3)

Bi-Lanczos-based methods: BI-CG and QMR, Bi-CGSTAB and CGS.

Day 5 Preconditioning Methods

Simple iterative methods as preconditioners. ILU, saddle-point preconditioning, etc.

The course consists of lectures and computer exercises, running each day from 9 a.m. to 4 p.m.

Course evaluation

Final evaluation will be based on a report which is agreed upon during the

course and which corresponds to about 30 hours of workload. The report

must be handed in no less than 4 weeks after completion of course.

Registration and deadline

Please sign up with Eva Rosenbaek: emr@imm.dtu.dk,

no later than October 10, 2008.

DTU Informatics: www.imm.dtu.dk.