In this paper, we consider the problem of the approximation of the integral of a function f over a d-dimensional simplex S of \(\mathbb {R}^{d}\) by some quadrature formulas which use only the functional and derivative values of f on the boundary of the simplex S or function data at the vertices of S, at points on its facets and at its center of gravity. The quadrature formulas are computed by integrating over S a polynomial approximant of f which uses functional and derivative values at the vertices of S.

中文翻译：

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关于d维单形上的一些数值积分公式。

在本文中，我们通过仅使用函数和导数的一些正交公式，考虑\（\ mathbb {R} ^ {d} \）的d维单形S上函数f的积分的逼近问题。在单纯形S的边界上的f的值或在S的顶点，其小平面上的点及其重心处的函数数据。正交公式通过在积分计算小号的多项式逼近˚F其在顶点使用功能性和导数值小号。