Padua点上的双变量拉格朗日插值：理想理论方法
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
AI总结：
本文从理想理论角度研究基于Padua点的双变量多项式插值，发现了插值多项式的紧凑公式，并分析了其L^p收敛性。
摘要：
Padua点是正方形$[-1,1]^2$上由显式公式给出的一族点，允许双变量多项式唯一拉格朗日插值。从理想理论的角度研究了基于Padua点的插值多项式和求积公式，从而发现了插值多项式的紧凑公式。还研究了插值多项式的$L^p$收敛性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
