An algorithm for a class of direct and inverse scattering problems

A novel, highly parallel algorithm for a class of direct and inverse scattering problems is proposed. It is shown that this algorithm reduces the noise propagation exhibited by the existing algorithms, and produces error terms that are proportional to the square of the discrete step size. Unlike the conventional algorithms, this new formulation decouples the reflection kernel in a given layer. Due to its decoupling nature, the new formulation completely eliminated any error propagation between any two points in the same layer. Numerical examples are presented to illustrate the proposed algorithm