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FSF3584 Preconditioning for Linear Systems 7.5 credits

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.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus FSF3584 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

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

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 disposition

Lectures, seminar, problem solving, problem composition.

Literature and preparations

Specific prerequisites

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.

Recommended prerequisites

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Equipment

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Literature

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

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

G

Examination

  • INL1 - Assignment, 7.5 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Problems solved, posed, seminar presented and homeworks solved.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

Profile picture Elias Jarlebring

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

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Offered by

SCI/Mathematics

Main field of study

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Education cycle

Third cycle

Add-on studies

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Contact

Elias Jarlebring (eliasj@kth.se)

Postgraduate course

Postgraduate courses at SCI/Mathematics