Pyramid algorithms for barycentric rational interpolation

摘要

We present a new perspective on the Floater-Hormann interpolant. This interpolant is rational of degree (n, d), reproduces polynomials of degree d, and has no real poles. By casting the evaluation of this interpolant as a pyramid algorithm, we first demonstrate a close relation to Neville's algorithm. We then derive an O(nd) algorithm for computing the barycentric weights of the Floater-Hormann interpolant, which improves upon the original O (nd~2) construction.