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252050400 G
Numerical Methods for Solving Large Scale Eigenvalue Problems
(Spring semester 2016)
Wednesday 10:1513:00, 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.
News
 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.
Contents
 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 JacobiDavidson Method
 Rayleigh quotient and trace minimization
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.
 Y. Saad: Numerical Methods for Large Eigenvalue Problems,
2nd revised edition. SIAM, Philadelphia, 2011.

G. W. Stewart. Matrix Algorithms II: Eigensystems.
SIAM, Philadelphia, 2001.
 G. H. Golub and Ch. van Loan: Matrix Computations, 4th edition.
Johns Hopkins University Press, Baltimore, 2012.
 B. N. Parlett: The Symmetric Eigenvalue Problem. Prentice
Hall, Englewood Cliffs, NJ, 1980. (Republished by SIAM, Philadelphia, 1998.)
Comments to arbenz@inf.ethz.ch
