An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems

Hammarling, Sven and Munro, Christopher J. and Tisseur, Francoise (2011) An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems. [MIMS Preprint]

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Abstract

We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable conditioning and backward stability properties, and a preprocessing step that reveals and deflates the zero and infinite eigenvalues contributed by singular leading and trailing matrix coefficients. The algorithm is backward stable for quadratics that are not too heavily damped. Numerical experiments show that our MATLAB implementation of the algorithm, quadeig, outperforms the MATLAB function polyeig in terms of both stability and efficiency.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Dr Françoise Tisseur
Date Deposited:	30 Apr 2012
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1815

Available Versions of this Item

• An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems. (deposited 25 Oct 2011)
  • An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems. (deposited 11 Dec 2011)
    • An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems. (deposited 30 Apr 2012) [Currently Displayed]
      • An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems. (deposited 08 Nov 2013)

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