The Neville‐like form of the Fitzpatrick algorithm for rational interpolation

The Fitzpatrick algorithm, which seeks a Gröbner basis for the solution of a system of polynomial congruences, can be applied to compute a rational interpolant. Based on the Fitzpatrick algorithm and the properties of an Hermite interpolation basis, we present a Neville‐like algorithm for multivariate osculatory rational interpolation. It may be used to compute the values of osculatory rational interpolants at some points directly without computing the rational interpolation function explicitly.