Error estimates of anti-Gaussian quadrature formulae

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• 作者：Miodrag M. Spalevi? ; ^{mspalevic@mas.bg.ac.rs}
• 关键词：primary ; 41A55 ; secondary ; 65D30 ; 65D32
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2012
• 出版时间：September, 2012
• 年：2012
• 卷：236
• 期：15
• 页码：3542-3555
• 全文大小：328 K

文摘

Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval . The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective -error bounds of anti-Gauss quadratures. Moreover, the effective -error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983)?, Gautschi et?al. (1990)? and Hunter (1995)? concerning Gaussian quadratures.