Model-Updating for Symmetric Quadratic Eigenvalue Problems

Lancaster, Peter (2006) Model-Updating for Symmetric Quadratic Eigenvalue Problems. [MIMS Preprint]

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Abstract

This paper concerns quadratic matrix functions of the form L(λ) = Mλ² + Dλ +K where M, D, K are real and symmetric n × n matrices with M > 0. Given complete spectral information on L(λ), it is shown how new systems of the same type can be generated with updated eigenvalues and/or eigenvectors. A general purpose algorithm is formulated and illustrated with problems having no real eigenvalues, or a mixture of real and non-real eiegnvalues, or only real eigenvalues. The methods also apply for matrix polynomials of higher degree.

Item Type: MIMS Preprint
Uncontrolled Keywords: Vibrating systems, updating, pole placement.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User: Ms Lucy van Russelt
Date Deposited: 27 Nov 2006
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/654

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