ETH Zürich

Prof. Dr. Peter Arbenz  


252-0504-00 G
Numerical Methods for Solving Large Scale Eigenvalue Problems
(Spring semester 2016)

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

First lecture: Wednesday February 24, 2016

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.


  • Lecture starts on February 24.
  • Lecture on April 13 is cancelled.
  • Final lecture on May 18. Final exercise lecture on May 25.
  • Examinations (30min oral) are planned for week of August 15.


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


  1. 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.
  2. Y. Saad: Numerical Methods for Large Eigenvalue Problems, 2nd revised edition. SIAM,  Philadelphia,  2011.
  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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