The Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation

In this paper, the authors first apply the Fitzpatrick algorithm to multivariate vector-valued osculatory rational interpolation. Then based on the Fitzpatrick algorithm and the properties of an Hermite interpolation basis, the authors present a Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation. It may be used to compute the values of multivariate vector-valued osculatory rational interpolants at some points directly without computing the interpolation function explicitly.