Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands
Apstrakt
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.
Ključne reči:
remainder term for analytic function / Legendre polynomials / Gauss quadrature formulae / error boundIzvor:
Electronic Transactions on Numerical Analysis, 2022, 55, 424-437Izdavač:
- Kent State University, Kent
Finansiranje / projekti:
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200105 (Univerzitet u Beogradu, Mašinski fakultet) (RS-MESTD-inst-2020-200105)
DOI: 10.1553/etna_vol55s424
ISSN: 1068-9613
WoS: 000813353900014
Scopus: 2-s2.0-85130081354
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Jandrlić, Davorka AU - KRTINić, D. M. AU - Mihić, Ljubica AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3783 AB - 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. PB - Kent State University, Kent T2 - Electronic Transactions on Numerical Analysis T1 - Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands EP - 437 SP - 424 VL - 55 DO - 10.1553/etna_vol55s424 ER -
@article{ author = "Jandrlić, Davorka and KRTINić, D. M. and Mihić, Ljubica and Pejčev, Aleksandar and Spalević, Miodrag", year = "2022", 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.", publisher = "Kent State University, Kent", journal = "Electronic Transactions on Numerical Analysis", title = "Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands", pages = "437-424", volume = "55", doi = "10.1553/etna_vol55s424" }
Jandrlić, D., KRTINić, D. M., Mihić, L., Pejčev, A.,& Spalević, M.. (2022). Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands. in Electronic Transactions on Numerical Analysis Kent State University, Kent., 55, 424-437. https://doi.org/10.1553/etna_vol55s424
Jandrlić D, KRTINić DM, Mihić L, Pejčev A, Spalević M. Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands. in Electronic Transactions on Numerical Analysis. 2022;55:424-437. doi:10.1553/etna_vol55s424 .
Jandrlić, Davorka, KRTINić, D. M., Mihić, Ljubica, Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds for gaussian quadrature formulae with legendre weight function for analytic integrands" in Electronic Transactions on Numerical Analysis, 55 (2022):424-437, https://doi.org/10.1553/etna_vol55s424 . .