## 2016.51: Strong linearizations of rational matrices

2016.51:
A. Amparan, F.M. Dopico, S. Marcaida and I. Zaballa
(2016)
*Strong linearizations of rational matrices.*

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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 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis MSC 2000 > 93 Systems theory; control |

MIMS number: | 2016.51 |

Deposited By: | Dr. Silvia Marcaida |

Deposited On: | 04 October 2016 |

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