Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Informatik
 
Abteilung V

 
Universität Bonn -> Institut für Informatik -> Abteilung V
CS-Reports 1985-1989 Copyright 1985-1989 Universität Bonn, Institut für Informatik, Abt. V
8538

10.12.2008

The Interpolation Problem for k-Sparse Sums of Eigenfunctions of Operators
Dima Grigoriev, Marek Karpinski and Miachel Singer
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In [DG 89], the authors show that many results concerning the problem of efficient interpolation of k-sparse multivariate polynomials can be formulated and proved in the general setting of k-sparse sums of characters of abelian monoids. In this note we describe another conceptual framework for the interpolation problem. In this framework, we consider R-algebras of functions A1,...,An on integral domain R, together with R-linear operators Di: AiAi. We then consider functions f from Rn to R that can be expressed as the sum of k terms, each term being an R-multiple of an n-fold product f1(x1)⋅...⋅fn(xn) where each fi is an eigenfunction for Di. We show how these functions can be thought of as k-sums of characters on an associated abelian monoid. This allows one to use the results of [DG 89] to solve interpolation problems for k-sparse sums of functions which, at first glance, do not seem to be characters.

Last Change: 12/10/08 at 16:58:49
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Universität Bonn -> Institut für Informatik -> Abteilung V

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