Pyramid algorithms for barycentric rational interpolation

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(nd2) construction.