An improved operator expansion algorithm for direct and inverse scattering computations

In the first part of the paper we present an implementation of Milder's operator expansion formalism for acoustic scattering from a rough non-periodic surface. Our main contribution to the forward-held calculation is the development of two accurate ways of computing the order-zero normal differentiation operator No. The accuracy of our implementation is tested numerically. In the second part of our paper we apply this approach, combined with a continuation method, to an inverse scattering problem. The resulting scheme performs significantly better than the classical first-order methods.