A note on “Error bounds of Gaussian quadrature formulae with Legendre weight function for analytic integrands” by M. M. Spalević et al.

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI:10.1553/etna_vol59s89

Aleksandar V. Pejčev

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引用次数: 1

Abstract

In paper D. Lj. ÄjukiÄ, R. M. MutavdÅ¾iÄ ÄjukiÄ, A. V. PejÄev, and M. M. SpaleviÄ, Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses â a survey of recent results, Electron. Trans. Numer. Anal., 53 (2020), pp. 352â382, Lemma 4.1 can be applied to show the asymptotic behaviour of the modulus of the complex kernel in the remainder term of all the quadrature formulas in the recent papers that are concerned with error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses. However, in the paper D. R. JandrliÄ, Dj. M. KrtiniÄ, Lj. V. MihiÄ, A. V. PejÄev, M. M. SpaleviÄ, Error bounds of Gaussian quadrature formulae with Legendre weight function for analytic integrands, Electron. Trans. Anal. 55 (2022), pp. 424â437, which this note is concerned with, there is a kernel whose numerator contains an infinite series, and in this case the mentioned lemma cannot be applied. This note shows that the modulus of the latter kernel attains its maximum as conjectured in the latter paper.

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M. M. spaleviki等人关于“解析积分的带Legendre权函数高斯正交公式的误差界”的注记。

论文中d.l j。Ä´jukiÄ°，R. M. MutavdÅ¾iÄ°Ä´jukiÄ°，a . V. PejÄ´ev, and M. M. SpaleviÄ°，椭圆上解析函数的高斯型正交公式的误差估计，最近结果的综述，电子。反式。号码。分析的在最近关于椭圆上解析函数的高斯型正交公式的误差估计的论文中，引理4.1可用于显示所有正交公式的余项中复核模的渐近行为。然而，在论文中d.r. JandrliÄ;M. KrtiniÄ;V. MihiÄ°n, A. V. PejÄ°n, M. M. SpaleviÄ°n，解析积分高斯正交公式与Legendre权函数的误差界，电子。反式。在本注注所讨论的(Anal. 55 (2022)， pp. 424 - ' 437)中，存在一个核，其分子包含一个无穷级数，在这种情况下，上述引理不能应用。这说明后一核的模达到了后一篇文章所推测的最大值。

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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来源期刊

Electronic Transactions on Numerical Analysis 数学-应用数学

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM).