- Iterative methods (Krylov methods, Gauss-Seidel methods)
- Convergence theory (eigenvalues, pseudospectra, right-hand side dependence)
- General preconditioners
- Problem specific preconditioners
FSF3584 Preconditioning for Linear Systems 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3584 (Spring 2019–)Headings with content from the Course syllabus FSF3584 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
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.
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.
Literature
It will be announced on the course web page 3 weeks before course starts
Examination and completion
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.
If the course is discontinued, students may request to be examined during the following two academic years.
Other requirements for final grade
Problems solved, posed, seminar presented and homeworks solved.
Examiner
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 room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle