## On Hermite interpolation in Rd

Boris Shekhtman

### Abstract

In this article, we deal with the problem of “Minimal Hermite Interpolation.” That is, given a number $k$ of distinct points in $R_d$ and the values of several derivatives at this point, we want to find a subspace of minimal dimension, where this interpolation problem has a solution, independent of the choice of points. In Section $2$, we present some results on such subspaces in the particular cases of two points and some or all partial derivatives of the first order. In Section $3$, we obtain some general upper bounds on the dimension of interpolation subspaces.

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### Key words

Hermite interpolation, Lagrange interpolation.

### AMS subject classifications

41A05, 41A63, 65D05.