On interpolation by radial polynomials
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Springer 2006
On interpolation by radial polynomials Carl de Boor PO Box 1076, Eastsound, WA 98245, U.S.A.
Received 15 April 2004; accepted 27 May 2004 Communicated by T. Sauer
Happy 60th and beyond, Charlie!
A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. Keywords: multivariate, polynomial, interpolation. Mathematics subject classifications (2000): 41A05, 41A6.
In his most-cited paper [3], Micchelli supplies the following interesting auxiliary lemma (his lemma 3.1). Lemma 1. If
n
i=1 ci p(xi )
= 0 for all p ∈
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