Computational Issues in Large Scale Eigenvalue Problems
Organizers
Peter Arbenz
Swiss Federal Institute of Technology (ETH),
Institute of Scientific Computing,
8092 Zurich, Switzerland
arbenz@inf.ethz.ch
and
Henk van der Vorst
Utrecht University,
Mathematical Institute,
3508 TA Utrecht,
The Netherlands
vorst@math.ruu.nl
Abstract
Many applications in science and industry require the solution of eigenvalue
problems for large matrices. Typically only a small fraction of the
eigenvalues together with their eigenvectors need to be computed, and this
makes the traditional methods, designed for dense small matrices, too
expensive.
In recent years new algorithms have been developed in addition to, or as
improvement of, the Lanczos and Arnoldi methods. These methods include:
- special restart strategies, in order to reduce the dimension of the search
space.
- spectral transformation techniques in order to obtain better convergence
towards wanted eigenvalues.
- alternative search subspaces, based on approximate shift-and-invert
techniques. In this class we find possibilities for preconditioning in
order to obtain efficient approximate inverse operations.
- parallel methods, including parallel techniques for the reduced
matrices.
- approaches for non-standard eigenproblems, such as constrained
eigenproblems and quadratic eigenproblems.
In this workshop we want to give an overview on recent progress in the
solution of large scale eigenvalue problems. Special emphasis is given on
the iterative solution and in the preconditioning of the linear systems,
associated with the approximate shift-and-invert methods (Jacobi-Davidson
and inexact shift-invert).
Presentations