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

Research paper by Len Bos, Stefano De Marchi, Marco Vianello, Yuan Xu

Indexed on: 27 Apr '06Published on: 27 Apr '06Published in: Mathematics - Numerical Analysis



Abstract

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.