Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function-Reference-Cited by-同舟云学术

Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function

Published:2020-05 Issue:2237 Volume:476 Page:20200099
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Adukov Victor M.¹^ORCID,Mishuris Gennady²^ORCID,Rogosin Sergei V.³^ORCID

Affiliation:

1. Institute of Natural Sciences and Mathematics, South Ural State University, 454080 Chelyabinsk, Russia

2. Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK

3. Department of Economics, Belarusian State University, 220030 Minsk, Belarus

Abstract

The possible instability of partial indices is one of the important constraints in the creation of approximate methods for the factorization of matrix functions. This paper is devoted to a study of a specific class of triangular matrix functions given on the unit circle with a stable and unstable set of partial indices. Exact conditions are derived that guarantee a preservation of the unstable set of partial indices during a perturbation of a matrix within the class. Thus, even in this probably simplest of cases, when the factorization technique is well developed, the structure of the parametric space (guiding the types of matrix perturbations) is non-trivial.

Funder

South Ural State University

Royal Society for the Wolfson Research Merit Award.

EPSRC grant

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2020.0099

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