A NOTE ON "ERROR BOUNDS OF GAUSSIAN QUADRATURE FORMULAE WITH LEGENDRE WEIGHT FUNCTION FOR ANALYTIC INTEGRANDS" BY M. M. SPALEVIĆ ET AL.(Article)(Open Access)
- Department of Mathematics, University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16 35, Belgrad, 11120, Serbia
Abstract
In paper D. LJ. DUKIĆ , R. M. MUTAVDŽIĆ DUKIĆ, 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. © 2023, Kent State University.
Indexed keywords
| Engineering controlled terms: | Functional analysisGaussian distribution |
|---|---|
| Engineering uncontrolled terms | Analytic functionsAsymptotic behaviourError boundError estimatesGaussian quadrature formulaGaussian type quadratureLegendreLegendre weight functionQuadrature formulaWeight functions |
| Engineering main heading: | Error analysis |
Funding details
| Funding sponsor | Funding number | Acronym |
|---|---|---|
| Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja | 451-03-9/2021-14/200105 | MPNTR |
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∗Received April 21, 2023. Accepted May 26, 2023. Published online on June 5, 2023. Recommended by L. Reichel. The research was supported in part by the Serbian Ministry of Education, Science and Technological Development, according to Contract 451-03-9/2021-14/200105 dated on February 5, 2021. †Department of Mathematics, University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrad 35, Serbia ([email protected]).
- ISSN: 10689613
- Source Type: Journal
- Original language: English
- DOI: 10.1553/etna_vol59s89
- Document Type: Article
- Publisher: Kent State University
Pejčev, A.V.; Department of Mathematics, University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16 35, Belgrad, Serbia;
© Copyright 2023 Elsevier B.V., All rights reserved.
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