Fast Non-Polynomial Interpolation of Functions with Logarithmic Singularities

The scattering characteristics of distributed soft targets are generally described by integral equations with singular kernels. For the purpose of fast computation of integrals of singular kernels, a fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularity. It can be executed efficiently with fast discrete cosine transforms. Interpolation errors of a manmade function, the well-known Hankel function of the first kind and the kernel-related function appeared in Hallen equation are shown as numerical examples to validate the efficiency of the proposed new interpolation.