On the structure of Kergin interpolation for points in general position

by Len Bos and Shayne Waldron


For $n+1$ points in $\Rd,$ in general position, the Kergin polynomial interpolant of $C^n$ functions may be extended to an interpolant of $C^{d-1}$ functions. This results in an explicit set of reduced Kergin functionals naturally stratified by their dependence on certain directional derivatives of order $k,$ $0\le k\le d-1.$ We show that the polynomials dual to the functionals depending on derivatives of order $k$ are multi-ridge functions of $d-k$ variables and moreover, that the polynomials dual to the purely interpolating functionals ($k=0$) are always harmonic.

Keywords: Kergin interpolation, multivariate interpolation

Math Review Classification: 41A05, 41A63, (primary), 41A10, 41A35 (secondary)

Length: 13 pages

Last updated: 27 April 2001

Status: accepted for the Bommerholz proceedings


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