Affiliation:
1. Institute of Natural Sciences and Mathematics, South Ural State University, Chelyabinsk 454080, Russia
2. Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK
Abstract
We discuss an explicit algorithm for solving the Wiener–Hopf factorization problem for matrix polynomials. Byan exact solutionof the problem, we understand the one constructed by a symbolic computation. Since the problem is, generally speaking, unstable, this requirement is crucial to guarantee that the result following from the explicit algorithm is indeed a solution of the original factorization problem. We prove that a matrix polynomial over the field of Gaussian rational numbers admits the exact Wiener–Hopf factorization if and only if its determinant is exactly factorable. Under such a condition, we adapt the explicit algorithm to the exact calculations and develop the ExactMPF package realized within the Maple Software. The package has been extensively tested. Some examples are presented in the paper, while the listing is provided in the electronic supplementary material. If, however, a matrix polynomial does not admit the exact factorization, we clarify a notion of the numerical (or approximate) factorization that can be constructed by following the explicit factorization algorithm. We highlight possible obstacles on the way and discuss a level of confidence in the final result in the case of an unstable set of partial indices. The full listing of the package ExactMPF is given in the electronic supplementary material.
Funder
Engineering and Physical Sciences Research Council
RFBR grant
H2020 Marie Skłodowska-Curie Actions
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
4 articles.
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