UNIVERSITY OF WISCONSIN-MADISON COMPUTER SCIENCES DEPARTMENT Computational aspects of polynomial interpolation in several variables

The pair 〈Θ, P 〉 of a pointset Θ ⊂ IR and a polynomial space P on IR is correct if the restriction map P → IR : p 7→ p|Θ is invertible, i.e., if there is, for any f defined on Θ, a unique p ∈ P which matches f on Θ. We discuss here a particular assignment Θ 7→ ΠΘ, introduced in [3], for which 〈Θ,ΠΘ〉 is always correct, and provide an algorithm for the contruction of a basis for ΠΘ which is related to Gauss elimination applied to the Vandermonde matrix (θα)θ∈Θ,α∈ZZd+ for Θ. We also discuss some attractive properties of the above assignment and algorithmic details of the algorithm, and present some bivariate examples. AMS (MOS) Subject Classifications: primary 41A05, 41A10, 41A63, 65D05, 65D15 secondary 15A12