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252050400 G
Numerical Methods for Solving Large Scale Eigenvalue Problems
(Spring semester 2018)
Wednesday 10:1513:00, 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
 There is no lecture on March 28.
 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 JacobiDavidson Method
 Rayleigh quotient and trace minimization
Literature
 Y. Saad: Numerical Methods for Large Eigenvalue Problems,
2nd revised edition. SIAM, Philadelphia, 2011.

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. 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
