An algorithm for computing the eigenvalues of a max-plus matrix polynomial

James, Hook (2016) An algorithm for computing the eigenvalues of a max-plus matrix polynomial. [MIMS Preprint]

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Abstract

Max-plus matrix polynomial eigenvalues provide a useful approximation to the order of magnitude of the eigenvalues of a classical (i.e. real or complex) matrix polynomial. In this paper we review the max-plus matrix eigensolver of Gassner and Klinz [1] and present our extension of this algorithm to the max-plus matrix polynomial case. Our max-plus matrix polynomial algo- rithm computes all nd max-plus eigenvalues of a n � n degree d max-plus matrix polynomial with worst case cost O(n3d) in the dense case, which is the best that we are aware of.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 49 Calculus of variations and optimal control; optimization MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Mr James Hook
Date Deposited:	05 Sep 2016
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2497

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