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Algorithms for solving large scale eigenvalue problems
Numerische Methoden für grosse Matrixeigenwertprobleme
Last Updated: 2026-02-05 15:19:52
Abstract
In this lecture algorithms are investigated for solving eigenvalue problemswith large sparse matrices. Some of these eigensolvers have been developedonly in the last few years. They will be analyzed in theory and practice (by meansof MATLAB exercises).
Objective
Knowing the modern algorithms for solving large scale eigenvalue problems, their numerical behavior, their strengths and weaknesses.
Content
The lecture starts with an introduction into the linear algebra of eigenvalue problems. Then the classical QR algorithm is treated. Afterwards, the most important algorithms for solving large scale, typically sparse matrix eigenvalue problems are introduced and analyzed. * vector and subspace iteration * trace minimization algorithm * Arnoldi and Lanczos algorithms (including restarting variants) * Davidson and Jacobi-Davidson Algorithm In the exercises, these algorithm will be implemented (in simplified forms) and analysed in MATLAB.
Resources
Lecture Notes
Copies of slides
Literature
Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000. G. H. Golub and Ch. van Loan: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore 1996.
General Information
- Language
- German
- Levels
- BSC , DS , MSC
- Frequency
- Every two years
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Numerische Methoden für grosse Matrixeigenwertprobleme
Does not take place this semester.
|
No time listed | 3 h weekly |