Factorization of a class of matrix-functions with stable partial indices

TL;DR

This paper introduces a new effective method for factorizing a specific class of nonrational matrix-functions with stable partial indices, extending previous work and demonstrating its efficiency through examples and numerical results.

Contribution

It generalizes a previous factorization method to a broader class of matrices with stable partial indices, applicable to practical problems.

Findings

The method effectively factorizes nonrational matrix-functions.

Numerical results confirm the efficiency of the proposed procedure.

Examples illustrate the properties and application of the asymptotic method.

Abstract

A new effective method for factorization of a class of nonrational $n\times n$ matrix-functions with \emph{stable partial indices} is proposed. The method is a generalization of the one recently proposed by the authors which was valid for the canonical factorization only. The class of considered matrices is motivated by problems originated from applications. The properties and details of the asymptotic procedure are illustrated by examples. The efficiency of the procedure is highlighted by numerical results.