A Class of Multivariate Rational Interpolation Formulas

Abstract

The object of this paper is to construct a class of multivariate rational interpolation formulas that can be used to solve interpolation problems with function data given at equidistant knots of various directed lines in the higher dimensional Euclidean space. Our formulas are built up of some explicit multivariate rational functions involving three sets of free parameters so that they enjoy sufficient flexibility for interpolating functions of several variables possessing certain kinds of singularities. The method adopted is an extension and modification of that described in our previous papers.