多节点高斯正交的Kronrod扩展

Computational Methods in Applied Mathematics Comput Pub Date : 1900-01-01 DOI:10.2478/CMAM-2006-0016

G. Milovanovi

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引用次数: 3

摘要

本文介绍了多节点高斯正交公式的一般实数Kronrod推广。给出了它们的存在唯一性的证明。在某些情况下，多项式的显式表达式，其零点是所考虑的正交的节点，是确定的。对共聚焦椭圆上解析函数，导出了具有Gori - michelli权函数的Gauss - Turan - Kronrod正交公式的非常有效的误差界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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KRONROD EXTENSIONS OF GAUSSIAN QUADRATURES WITH MULTIPLE NODES

In this paper, general real Kronrod extensions of Gaussian quadrature formulas with multiple nodes are introduced. A proof of their existence and uniqueness is given. In some cases, the explicit expressions of polynomials, whose zeros are the nodes of the considered quadratures, are determined. Very effective error bounds of the Gauss — Turan — Kronrod quadrature formulas, with Gori — Micchelli weight functions, for functions analytic on confocal ellipses, are derived.

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Computational Methods in Applied Mathematics Comput

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