FAST PRECONDITIONED CONJUGATE-GRADIENT ALGORITHMS FOR WIENER-HOPF INTEGRAL-EQUATIONS

In this paper the authors study circulant approximations of finite sections of a Wiener-Hopf integral equation on the half-line. Such circulant, operators are defined by periodic kernel functions. They approximate finite sections of the Wiener Hopf operator within a sum of a small operator and an operator with fixed finite rank. Constructions are given of two such circulant operators and their use as preconditioners for the Conjugate Gradients algorithm is explained. Numerical examples are included to illustrate the results.