Approximate Wiener--Hopf Factorisation with Stability Analysis

This thesis is split into four sections which are outlined below. The first section describes therelationship between the line Riemann–Hilbert problem and a strip Wiener–Hopf problem.This is used to examine the stability of the scalar Wiener–Hopf equations in the subsequentsection. New approximate factorisations are proposed based on conformal mappings andRational Carathéodory–Fejér Approximation. The next section generalises the approximationprocedure to the important class of Daniele–Khrapkov matrices. Finally, the ideas are applied to approximate the matrix resulting from sound scattering from an infinite grating