On multivariate Hermite interpolation (Q1904141)

The authors study the problem of Hermite interpolation by polynomials in several variables. They adopt a very general formulation of this problem, consisting in interpolation of consecutive chains of directional derivatives. By using the notion of blockwise structure introduced by the authors in a previous paper [Math. Comp. (to appear)], they establish an interpolation formula analogous to that of Newton in one variable and use it for obtaining an integral representation for the remainder. In order to illustrate the various definitions and results, numerous examples are presented throughout the paper.