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

In this paper the authors study circulant approximations of finite sec tions of a Wiener-Hopf integral equation on the half-line. Such circul ant, operators are defined by periodic kernel functions. They approxim ate finite sections of the Wiener Hopf operator within a sum of a smal l operator and an operator with fixed finite rank. Constructions are g iven 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.