Genuine-optimal circulant preconditioners for Wiener-Hopf equations (Q2770167)

The author constructs a genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. This preconditioner is defined as the minimizer of the Hilbert-Schmidt norm for certain integral operators. It is proved that the difference between this preconditioner and the original integral operator is the sum of a small norm operator and a finite rank operator. From this follows that the preconditioned conjugate gradient method converges superlinearly if it is applied for solving the preconditioned equations. An efficient algorithm for the solution of Wiener-Hopf equation which is discretized by high order quadrature rules is given.