A Convergent Family of Bivariate Floater-Hormann Rational Interpolants

Abstract

It is well-known that the Floater-Hormann rational interpolants give better results than other rational interpolants, especially in convergence rates and barycentric form. In this paper, we propose and study a family of bivariate Floater-Hormann rational interpolants, which have no real poles and arbitrarily high convergence rates on any rectangular region. Moreover, these interpolants are linear on data. In the end, several numerical examples further confirm our results.