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https://research.matf.bg.ac.rs/handle/123456789/2979| Title: | Error bounds of Gaussian quadrature formulae with Legendre weight function for analytic integrands | Authors: | Jandrlić, D. R. Krtinić, Đorđe Mihić, L. J.V. Pejčev, A. V. Spalević, M. M. |
Affiliations: | Real and Functional Analysis | Keywords: | error bound;Gauss quadrature formulae;Legendre polynomials;remainder term for analytic function | Issue Date: | 1-Jan-2021 | Rank: | M22 | Publisher: | Kent State University | Journal: | Electronic Transactions on Numerical Analysis | Abstract: | In this paper we are concerned with a method for the numerical evaluation of the error terms in Gaussian quadrature formulae with the Legendre weight function. Inspired by the work of H. Wang and L. Zhang [J. Sci. Comput., 75 (2018), pp. 457–477] and applying the results of S. Notaris [Math. Comp., 75 (2006), pp. 1217–1231], we determine an explicit formula for the kernel. This explicit expression is used for finding the points on ellipses where the maximum of the modulus of the kernel is attained. Effective error bounds for this quadrature formula for analytic integrands are derived. |
URI: | https://research.matf.bg.ac.rs/handle/123456789/2979 | DOI: | 10.1553/etna_vol55s424 |
| Appears in Collections: | Research outputs |
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