Adaptive inverse quadratics interpolation with applications to Vector Fitting and the Hankel transform of spectral domain Green's functions

In this contribution we discuss the translation-invariant interpolation of univariate functions by means of inverse quadratics radial basis functions. For the implementation we use an adaptive interpolation process which is a variant of a recently introduced adaptive residual subsampling method. It is shown that the interpolation process with the inverse quadratics kernel also provides an excellent pre-processing interface when used in conjunction with the popular Vector Fitting algorithm. This results in a composite algorithm, performing the sampling and modelling of the given function in a fully automatic way. It also provides a platform for calculating the Hankel transform of spectral domain Green's functions.