INTERNALITY OF GENERALIZED AVERAGED GAUSS RULES AND THEIR TRUNCATIONS FOR BERNSTEIN-SZEGŐ WEIGHTS∗
INTERNALITY OF GENERALIZED AVERAGED GAUSS RULES AND THEIR TRUNCATIONS FOR BERNSTEIN-SZEGŐ WEIGHTS∗
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广义平均高斯规则的内在性及其对 Bernstein-SZEGŐ 权重的截断*
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
J. Tomanovic
中科院分区：
文献类型：
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作者：
D. Djukić;L. Reichel;M. Spalević;J. Tomanovic
广义平均高斯求积公式可以有积分区间以外的节点。积分区间外节点的求积规则不能应用于被积函数仅定义在积分区间上的近似积分。本文研究了Bernstein-SzegIgnweight函数的广义平均Gauss求积法则的所有节点都在积分区间内的情形。也被认为是截断这些正交规则的变种。探讨了广义平均Gauss求积公式与Gauss-Kronrod规则之间的关系。
Generalized averaged Gauss quadrature formulas may have nodes outside the interval of integration. Quadrature rules with nodes outside the interval of integration cannot be applied to approximate integrals with an integrand that is defined on the interval of integration only. This paper investigates when generalized averaged Gauss quadrature rules for Bernstein-Szegő weight functions have all nodes in the interval of integration. Also truncated variants of these quadrature rules are considered. The relation between generalized averaged Gauss quadrature formulas and Gauss-Kronrod rules is explored.