Bivariate Lagrange interpolation at the Padua points: Computational aspects

[摘要] The so-called Padua points give a simple, geometric and explicit construction of bivariate polynomial interpolation in the square. Moreover, the associated Lebesgue constant has minimal order of growth O(log(2)(n)). Here we show four families of Padua points for interpolation at any even or odd degree n, and we present a stable and efficient implementation of the corresponding Lagrange interpolation formula, based on the representation in a suitable orthogonal basis. We also discuss extension of (nonpolynomial) Padua-like interpolation to other domains, such as triangles and ellipses; we give complexity and error estimates, and several numerical tests. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2008-11-15

[效力级别]  Proceedings Paper

[关键词] Bivariate polynomial interpolation;Square;Padua points;Bivariate Chebyshev orthogonal polynomials;Reproducing kernel