ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Aleksandar V. Pejčev
S. 89 - 98 doi:10.1553/etna_vol59s89 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol59s89
Abstract: In paper D. Lj. Đjukić, R. M. Mutavdžić Đjukić, A. V. Pejčev, and M. M. Spalević, Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses – a survey of recent results, Electron. Trans. Numer. Anal., 53 (2020), pp. 352–382, 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. Jandrlić, Dj. M. Krtinić, Lj. V. Mihić, A. V. Pejčev, M. M. Spalević, Error bounds of Gaussian quadrature formulae with Legendre weight function for analytic integrands, Electron. Trans. Anal. 55 (2022), pp. 424–437, 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. Keywords: error bound, quadrature formula, Legendre weight function Published Online: 2023/06/05 12:44:55 Object Identifier: 0xc1aa5576 0x003e486e Rights: . 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). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |