On the Structure of Fully Symmetric Multidimensional Quadrature Rules
On the Structure of Fully Symmetric Multidimensional Quadrature Rules
复制标题
论全对称多维求积规则的结构
DOI：
10.1137/0716002
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发表时间：
1979
影响因子：
2.9
通讯作者：
J. N. Lyness
中科院分区：
文献类型：
--
作者：
P. Keast;J. N. Lyness
构造完全对称积分区域的指定适度多项式次数的完全对称求积规则的一种方法包括直接求解定义问题的可能大的矩拟合方程组。在最近的一篇基础论文中，Mantel和Rabinowitz [4]（SIAM J. Numer.分析：1977年）在三维背景下处理了这个问题的一些细节。他们定义并计算了一组相容性条件，并利用这些条件，在很大程度上系统化了二维和三维完全对称求积规则的现有技术。本文是对[4]的补充。我们引入一组零空间。使用这些，通常冗长的一致性条件的计算可以以使人为错误明显更不可能的方式减少到自动线性过程。此外，这些空间可用于计算的实际组织中。
One method for constructing fully symmetric quadrature rules of specified moderate polynomial degree for fully symmetric integration regions consists of solving directly the possibly large system of moment fitting equations which define the problem. A familiar hazard is to find these equations are inconsistent.In a recent fundamental paper, Mantel and Rabinowitz [4] (SIAM J. Numer. Anal., 1977) treated this problem in some detail in a three dimensional context. They defined and calculated a set of consistency conditions and using these, systematized to a significant extent the present state of the art for two and three dimensional fully symmetric quadrature rules.This paper is complementary to [4]. We introduce a set of null spaces. Using these, the calculations of the consistency conditions which is in general tedious, can be reduced to an automatic linear procedure in a way which makes human error significantly less likely. In addition, these spaces may be used in the actual organization of a calculatio...