Stability Analysis of Matrix Wiener--Hopf Factorisation of Daniele--Khrapkov Class and Reliable Approximate Factorisation

TL;DR

This paper investigates the stability of matrix Wiener--Hopf factorisation within the Daniele--Khrapkov class and explores reliable approximate factorisation methods, supported by numerical examples demonstrating various partial indices.

Contribution

It provides new stability conditions for Wiener--Hopf factorisation in the Daniele--Khrapkov class and introduces methods for approximate factorisation of related matrix functions.

Findings

Stability conditions for Wiener--Hopf factorisation established

Methods for approximate factorisation demonstrated

Numerical examples validate theoretical results

Abstract

This paper presents new stability results for matrix Wiener--Hopf factorisation. The first part of the paper examines conditions for stability of Wiener-Hopf factorisation in Daniele--Khrapkov class. The second part of the paper concerns the class of matrix functions which can be exactly or approximately reduced to the factorisation of the Daniele--Khrapkov matrices. The results of the paper are demonstrated by numerical examples with partial indices \(\{1,-1\}\), \(\{0,0\}\) and \(\{-1,-1\}\).