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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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|
submitted to SIAM J. Matrix Anal. Appl. (revised version)
|Uncontrolled Keywords:||polynomial eigenvalue problem, balancing, scaling, condition number, backward error|
|Subjects:||MSC 2000 > 65 Numerical analysis|
|Deposited By:||Dr. Timo Betcke|
|Deposited On:||10 April 2008|
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