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 statespace 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 selfcontained as possible.
Item Type:  MIMS Preprint 

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:  27 Mar 2018 23:16 
Last Modified:  27 Mar 2018 23:16 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/2631 
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Strong linearizations of rational matrices. (deposited 04 Oct 2016)
 Strong linearizations of rational matrices. (deposited 27 Mar 2018 23:16) [Currently Displayed]
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