Error bounds of the Micchelli-Sharma quadrature formula for analytic functions
Апстракт
Micchelli and Sharma constructed in their paper [On a problem of Turan: multiple node Gaussian quadrature, Rend. Mat. 3 (1983) 529-552] a quadrature formula for the Fourier-Chebyshev coefficients, which has the highest possible precision. For analytic functions the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points not equal 1 and a sum of semi-axes rho > 1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the location on the ellipses where the maximum modulus of the kernel is attained, and derive effective error bounds for this quadrature formula. Numerical examples are included.
Кључне речи:
Micchelli-Sharma quadrature formula / Error bound / Contour integral representationИзвор:
Journal of Computational and Applied Mathematics, 2014, 259, 48-56Издавач:
- Elsevier Science Bv, Amsterdam
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1016/j.cam.2013.03.039
ISSN: 0377-0427
WoS: 000329376600006
Scopus: 2-s2.0-84887492806
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1876 AB - Micchelli and Sharma constructed in their paper [On a problem of Turan: multiple node Gaussian quadrature, Rend. Mat. 3 (1983) 529-552] a quadrature formula for the Fourier-Chebyshev coefficients, which has the highest possible precision. For analytic functions the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points not equal 1 and a sum of semi-axes rho > 1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the location on the ellipses where the maximum modulus of the kernel is attained, and derive effective error bounds for this quadrature formula. Numerical examples are included. PB - Elsevier Science Bv, Amsterdam T2 - Journal of Computational and Applied Mathematics T1 - Error bounds of the Micchelli-Sharma quadrature formula for analytic functions EP - 56 SP - 48 VL - 259 DO - 10.1016/j.cam.2013.03.039 ER -
@article{ author = "Pejčev, Aleksandar and Spalević, Miodrag", year = "2014", abstract = "Micchelli and Sharma constructed in their paper [On a problem of Turan: multiple node Gaussian quadrature, Rend. Mat. 3 (1983) 529-552] a quadrature formula for the Fourier-Chebyshev coefficients, which has the highest possible precision. For analytic functions the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points not equal 1 and a sum of semi-axes rho > 1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the location on the ellipses where the maximum modulus of the kernel is attained, and derive effective error bounds for this quadrature formula. Numerical examples are included.", publisher = "Elsevier Science Bv, Amsterdam", journal = "Journal of Computational and Applied Mathematics", title = "Error bounds of the Micchelli-Sharma quadrature formula for analytic functions", pages = "56-48", volume = "259", doi = "10.1016/j.cam.2013.03.039" }
Pejčev, A.,& Spalević, M.. (2014). Error bounds of the Micchelli-Sharma quadrature formula for analytic functions. in Journal of Computational and Applied Mathematics Elsevier Science Bv, Amsterdam., 259, 48-56. https://doi.org/10.1016/j.cam.2013.03.039
Pejčev A, Spalević M. Error bounds of the Micchelli-Sharma quadrature formula for analytic functions. in Journal of Computational and Applied Mathematics. 2014;259:48-56. doi:10.1016/j.cam.2013.03.039 .
Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds of the Micchelli-Sharma quadrature formula for analytic functions" in Journal of Computational and Applied Mathematics, 259 (2014):48-56, https://doi.org/10.1016/j.cam.2013.03.039 . .