SF3584 Preconditioning for Linear Systems 7.5 credits

Förkonditionering för linjära ekvationssystem

Linear system of equations form one of the most fundamental problem classes in computation in science and engineering. Many linear systems of equations stemming from applications are expressed in terms of large sparse matrices, which are solved by iterative algorithms. The purpose of this course is to learn about the iterative algorithms for large-scale linear systems and how to improve them by using matrix structures and the techniques called preconditioning.

  • Education cycle

    Third cycle
  • Main field of study

  • Grading scale

Information for research students about course offerings

Spring 2018

Intended learning outcomes

A students which has passed this course should know

  • which iterative methods are available for linear systems, and integration of preconditioning.

  • how to apply and adapt convergence theory for the iterative methods.

  • apply general preconditioners based on, diagonal, LU-factorization.

  • apply problem specific preconditioners, such as domain decomposition, Schur-complement and adapted for partial differential equations such as Helmholtz problem.

  • characterize the quality of a preconditioner experimentally and theoretically.

Course main content

  1. Iterative methods (Krylov methods, Gauss-Seidel methods)
  2. Convergence theory (eigenvalues, pseudospectra, right-hand side dependence)
  3. General preconditioners
  4. Problem specific preconditioners

Disposition

Lectures, seminar, problem solving, problem composition

Eligibility

This course is designed for PhD students in applied and computational mathematics, but it is suitable also for other PhD students with a background in computation with mathematical interests. The students are expected to have taken a basic and a continuation course in numerical analysis or acquired equivalent knowledge in a different way, and preferrably also a course in matrix computations or numerical linear algebra, e.g., SF3580 and/or SF2524.

Literature

It will be announced on the course web page 3 weeks before course starts

Examination

Requirements for final grade

Problems solved, posed, seminar presented and homeworks solved

Offered by

SCI/Mathematics

Contact

Elias Jarlebring (eliasj@kth.se)

Examiner

Elias Jarlebring <eliasj@kth.se>

Version

Course syllabus valid from: Spring 2018.