Amparan, A. and Dopico, F.M. and Marcaida, S. and Zaballa, I.
(2016)
*Strong linearizations of rational matrices.*
[MIMS Preprint]

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## Abstract

This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and diferent characterizations of such linear matrix pencils, and develops infinitely many examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper part of the considered rational matrix and the coefficients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both finite and at infinity, of any rational matrix by applying any well known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations explicitly constructed in this work. Since the results of this paper require to use several concepts that are not standard in matrix computations, a considerable effort has been done to make the paper as self-contained as possible.

Item Type: | MIMS Preprint |
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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 > 93 Systems theory; control |

Depositing User: | Dr. Silvia Marcaida |

Date Deposited: | 04 Oct 2016 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2506 |

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