Abstract:This article obtains specific formulas for Lagrange polynomials for rectangular versions of the even and the odd product nodes in $\mathbb {R}^2$. These polynomials are applied to obtain an exact cubature formula for bivariate polynomials when the number of rows of the nodes exceeds the number of columns by one.

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中文翻译：

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矩形节点集的插值和体积

摘要：本文获得了 $\mathbb {R}^2$ 中偶数和奇数乘积节点的矩形版本的拉格朗日多项式的具体公式。当节点的行数超过列数一时，应用这些多项式来获得二元多项式的精确体积公式。

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