# An Iterative Wiener--Hopf method for triangular matrix functions with exponential factors

## TL;DR

This paper presents an iterative Wiener--Hopf method for approximating solutions to a class of equations involving triangular matrix functions with exponential factors, enabling controlled error reduction and practical application in acoustics.

## Contribution

It introduces a novel iterative approach generalizing pole removal techniques for Wiener--Hopf equations with explicit error estimates and efficient convergence.

## Key findings

- Error can be explicitly estimated and minimized.
- Few iterations suffice for practical accuracy.
- Method successfully applied to acoustics problems.

## Abstract

This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations, at the moment, cannot be obtained. The proposed method could be considered as a generalisation of the pole removal technique. The error in the approximation can be explicitly estimated, and by a sufficient number of iterations could be made arbitrary small. Typically only a few iterations are required for practical purposes. The theory is illustrated by numerical examples that demonstrate the advantages of the proposed procedure. This method was motivated and successfully applied to problems in acoustics.