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

2006/04/27 by Len Bos, Bos, Len, Stefano De Marchı +5 · 1 citation
Engineering · Mathematics · #41A05 #41A10 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.math/0604604

openalex publication_date 2006/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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