ETH Zürich

Prof. Dr. Peter Arbenz  

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252-0504-00 G
Numerical Methods for Solving Large Scale Eigenvalue Problems
(Spring semester 2018)

Wednesday 10:15-13:00, ML H43
Type of lecture G3, 4 ETCS credit points

First lecture: Wednesday February 21, 2018


Algorithms are investigated for solving eigenvalue problems with large sparse matrices. Some of these eigensolvers have been developed only in the last few years. They will be analyzed in theory and practice (by means of MATLAB exercises).

Lecture notes are available from this web site.



News

  • Lecture starts on Wednesday February 21.
  • Final lecture will be on May 23.
  • Examinations (30min oral) are planned for the first week of June.

Contents

  • Introduction
  • Some linear algebra basics
  • The QR Algorithm
  • Vector iteration (power method) and relatives
  • Subspace iterations (simultaneous vector iterations)
  • Krylov subspaces
  • Arnoldi and Lanczos algorithms
  • Restarting Arnoldi and Lanczos algorithms
  • The Jacobi-Davidson Method
  • Rayleigh quotient and trace minimization
 

Literature

  1. Y. Saad: Numerical Methods for Large Eigenvalue Problems, 2nd revised edition. SIAM,  Philadelphia,  2011.
  2. 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.
  3. G. W. Stewart. Matrix Algorithms II: Eigensystems. SIAM,  Philadelphia,  2001.
  4. G. H. Golub and Ch. van Loan: Matrix Computations, 4th edition. Johns Hopkins University Press,  Baltimore,  2012.
  5. B. N. Parlett: The Symmetric Eigenvalue Problem. Prentice Hall, Englewood Cliffs, NJ, 1980. (Republished by SIAM, Philadelphia, 1998.)


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