Bivariate Lagrange interpolation at the Padua points: the ideal theory approach

Authors:
Len Bos;Stefano De Marchi;Marco Vianello;Yuan Xu
Affiliations:
University of Calgary, Department of Mathematics and Statistics, Calgary, AB, Canada;University of Verona, Department of Computer Science, Verona, 37134, AB, Italy;University of Padua, Department of Pure and Applied Mathematics, 35131, Padua, AB, Italy;University of Oregon, Department of Mathematics, 97403-1222, Eugene, OR, USA
Venue:
Numerische Mathematik
Year:
2007

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Abstract

The Padua points are a family of points on the square [−1, 1]2 given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. Interpolation polynomials and cubature formulas based on the Padua points are studied from an ideal theoretic point of view, which leads to the discovery of a compact formula for the interpolation polynomials. The Lp convergence of the interpolation polynomials is also studied.