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.
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
DE MARCHI, STEFANO;VIANELLO, MARCO;
2007
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.
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