Error bounds for Gaussian quadrature formulae with Legendre weight function for analytic integrands. ETNA - Electronic Transactions on Numerical Analysis
Fiche du document
13 avril 2022
- handle: 10670/1.btctqf
- issn: 1068-9613
- doi: 10.1553/etna_vol55s424
info:eu-repo/semantics/openAccess
Sujets proches
Weight and measurementCiter ce document
A. V. Pejčev et al., « Error bounds for Gaussian quadrature formulae with Legendre weight function for analytic integrands. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol55s424
Métriques
Partage / Export
Résumé
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.