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Multivariate polynomial interpolation over arbitrary grids

Research paper by Vesa Kaarnioja

Indexed on: 23 Dec '15Published on: 23 Dec '15Published in: Mathematics - Numerical Analysis



Abstract

In this work, a new algorithm is presented for multivariate polynomial interpolation over arbitrary nodal sets. The method is based on selecting a basis for the interpolating polynomial through sequential maximization of the Vandermonde volume, which is shown in this paper to yield an upper bound on the associated Lebesgue constant. For general nodal sets, the interpolating polynomial produced by the proposed algorithm aims to minimize the Lebesgue constant at each step and thus promotes accuracy for non-poised interpolation problems. The algorithm behaves well even when the nodal set is singular in terms of classical polynomial interpolation. These assertions are verified in the numerical experiments.