Barycentric prolate interpolation and pseudospectral differentiation

Abstract

In this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

Efficient Methods for the Chebyshev-Type Prolate Spheroidal Wave Functions and Corresponding Eigenvalues

“…Remark 1. As demonstrated in [38] for the PSWF case, we introduced Barycentric prolate interpolation and differentiation, which is essential in various applications of spectral methods. One crucial aspect is the computation of prolate barycentric weights.…”