A Recursive Computation Scheme for Multivariate Rational Interpolants

Abstract

We derive here a recursive computation scheme for the rational interpolation method introduced in [7]. Explicit formulas for these multivariate rational interpolants are repeated in § 2 while the recursive algorithm is described in § 3. A number of interesting special cases such as the univariate rational interpolation problem and the multivariate Padé approximants introduced in [6] and [10] are dealt with in § 4. For some of these rational approximants other recursive schemes were described previously. Finally § 5 contains the numerical results: the multivariate rational interpolants described here are compared with multivariate polynomial interpolants, interpolating branched continued fractions introduced by Cuyt and Verdonk [8], interpolating branched continued fractions introduced by Siemaszko [12] and several multivariate Padé approximants [6], [3], [10]. Besides the fact that our multivariate rational interpolants allow a large degree of freedom in the choice for the numerator and denominator in order to fit the function to be approximated as well as possible, they also produce very accurate numerical results.