On the structure of Kergin interpolation for points
in general position
by Len Bos and Shayne Waldron
Abstract:
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
Availability:
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