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

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

2006-04-27

arxiv.org/abs/math/0604604v1

Mathematics

Numerical Analysis

11 pages

Scientific paper

Padua points is a family of points on the square $[-1,1]^2$ given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The 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 $L^p$ convergence of the interpolation polynomials is also studied.

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