Interpolation to boundary data on the simplex (Q1068506)

The author develops an explicit representation of a finite-dimensional Hermite polynomial interpolant for the simplex in \(R^ n\) which matches the function and certain derivative values at its vertices. The basis functions of this scheme are then used in the construction of a \(C^ N\) blending function interpolant (for an appropriate N) for the simplex which matches an infinite set of data (function and derivative values given on all the faces). The scheme for the triangle was first described by the author [Multivariate approximation, Symp. Univ. Durham 1977, 279- 288 (1978; Zbl 0458.65004)] and some results in tetrahedra by \textit{L. Mansfield} [J. Math. Anal. Appl. 56, 137-164 (1976; Zbl 0361.41002)].