Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems |
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| Authors: | Gerard L G Sleijpen Albert G L Booten Diederik R Fokkema Henk A van der Vorst |
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| Institution: | (1) Mathematical Institute, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands;(2) CWI, P.O. Box 94079, NL-1090 GB Amsterdam, The Netherlands;(3) Present address: Integrated Systems Engineering AG, Technopark Zürich, Technoparkstrasse 1, CH-8005 Zürich, Switzerland |
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| Abstract: | In this paper we will show how the Jacobi-Davidson iterative method can be used to solve generalized eigenproblems. Similar ideas as for the standard eigenproblem are used, but the projections, that are required to reduce the given problem to a small manageable size, need more attention. We show that by proper choices for the projection operators quadratic convergence can be achieved. The advantage of our approach is that none of the involved operators needs to be inverted. It turns out that similar projections can be used for the iterative approximation of selected eigenvalues and eigenvectors of polynomial eigenvalue equations. This approach has already been used with great success for the solution of quadratic eigenproblems associated with acoustic problems.Our friend Albert died on November 12, 1995 |
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| Keywords: | Eigenvalues and eigenvectors eigenproblem generalized eigenproblem quadratic eigenproblem polynomial eigenproblem Jacobi-Davidson method Ritz values harmonic Ritz values |
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