Higher-order quadratures for circulant preconditioned Wiener-Hopf equations (Q1913588)

A new preconditioner for Wiener-Hopf equations is developed to avoid matrix systems that cannot be solved efficiently by using fast Fourier transforms when higher order quadratures are employed to discretize the preconditioned equations. The preconditioner proposed here is produced by using self-adjoint circulant integral operators to precondition the integral operators of the Wiener-Hopf equation. The spectra of the circulant preconditioned operator are clustered around 1, so that the preconditioned conjugate gradient method converges fast. Numerical examples are given, unfortunately the error analysis is not elaborated very carefully.