2007.120: Optimal scaling of generalized and polynomial eigenvalue problems
2007.120: T. Betcke (2007) Optimal scaling of generalized and polynomial eigenvalue problems.
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Abstract
Scaling is a commonly used technique for standard eigenvalue problems to improve the sensitivity of the eigenvalues. In this paper we investigate scaling for generalized and polynomial eigenvalue problems (PEPs) of arbitrary degree. It is shown that an optimal diagonal scaling of a PEP with respect to an eigenvalue can be described by the ratio of its normwise and componentwise condition number. Furthermore, the effect of linearization on optimally scaled polynomials is investigated. We introduce a generalization of the diagonal scaling by Lemonnier and Van Dooren to PEPs that is especially effective if some information about the magnitude of the wanted eigenvalues is available and also discuss variable transformations of the type λ = αμ for PEPs of arbitrary degree.
| Item Type: | MIMS Preprint |
|---|---|
| Additional Information: | submitted to SIAM J. Matrix Anal. Appl. |
| Uncontrolled Keywords: | polynomial eigenvalue problem, balancing, scaling, condition number, backward error |
| Subjects: | MSC 2000 > 65 Numerical analysis |
| MIMS number: | 2007.120 |
| Deposited By: | Dr. Timo Betcke |
| Deposited On: | 08 October 2007 |
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- Optimal scaling of generalized and polynomial eigenvalue problems (deposited 10 April 2008)
- Optimal scaling of generalized and polynomial eigenvalue problems (deposited 08 October 2007) [Currently Displayed]
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