On convergence rates of prolate interpolation and differentiation

Prolate spheroidal wave functions of order zero (PSWFs) are widely used in scientific computation. There are few results about the error bounds of the prolate interpolation and differentiation. In this paper, based on the Cauchy’s residue theorem and asymptotics of PSWFs, the convergence rates are derived. To get stable approximation, the first barycentric formula is applied. These theoretical results and high accuracy are illustrated by numerical examples.