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Consistent structures of invariant quadrature rules for the $n$-simplex

Authors: J. I. Maeztu and E. Sáinz de la Maza
Journal: Math. Comp. 64 (1995), 1171-1192
MSC: Primary 65D32
MathSciNet review: 1297473
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Abstract: In this paper we develop a technique to obtain, in a systematic way, the consistency conditions for the n-dimensional simplex ${T_n}$ for any dimension n and degree of precision d. The introduction of a convenient basis of invariant polynomials provides a powerful tool to analyze and obtain consistent structures. We also present tables listing the optimal consistent structures for dimensions $n = 2, \ldots ,8$ and degree of precision up to $d = 23$. This paper is devoted only to structures. No quadrature rules are presented here.

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Keywords: Invariant quadrature rule, consistency conditions, simplex, consistent structure, multidimensional quadrature
Article copyright: © Copyright 1995 American Mathematical Society