Error bounds of Micchelli-Rivlin quadrature formula for analytic functions
2013
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We consider the well known Micchelli-Rivlin quadrature formula, of highest algebraic degree of precision, for the Fourier-Chebyshev coefficients. 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 -/+ 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 locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective L-infinity-error bounds for this quadrature formula. Complex-variable methods are used to obtain expansions of the error in the Micchelli-Rivlin quadrature formula over the interval [-1, 1]. Finally, effective L-1-error bounds are also derived for this quadrature formula.
Ključne reči:
Remainder term for analytic functions / Micchelli-Rivlin quadrature formula / Error bound / Contour integral representation / Chebyshev weight function of the first kindIzvor:
Journal of Approximation Theory, 2013, 169, 23-34Izdavač:
- Academic Press Inc Elsevier Science, San Diego
Finansiranje / projekti:
- Metode numeričke i nelinearne analize sa primenama (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1016/j.jat.2013.02.002
ISSN: 0021-9045
WoS: 000318332100003
Scopus: 2-s2.0-84875260126
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Institucija/grupa
Mašinski fakultetTY - JOUR AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1672 AB - We consider the well known Micchelli-Rivlin quadrature formula, of highest algebraic degree of precision, for the Fourier-Chebyshev coefficients. 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 -/+ 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 locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective L-infinity-error bounds for this quadrature formula. Complex-variable methods are used to obtain expansions of the error in the Micchelli-Rivlin quadrature formula over the interval [-1, 1]. Finally, effective L-1-error bounds are also derived for this quadrature formula. PB - Academic Press Inc Elsevier Science, San Diego T2 - Journal of Approximation Theory T1 - Error bounds of Micchelli-Rivlin quadrature formula for analytic functions EP - 34 SP - 23 VL - 169 DO - 10.1016/j.jat.2013.02.002 ER -
@article{ author = "Pejčev, Aleksandar and Spalević, Miodrag", year = "2013", abstract = "We consider the well known Micchelli-Rivlin quadrature formula, of highest algebraic degree of precision, for the Fourier-Chebyshev coefficients. 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 -/+ 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 locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective L-infinity-error bounds for this quadrature formula. Complex-variable methods are used to obtain expansions of the error in the Micchelli-Rivlin quadrature formula over the interval [-1, 1]. Finally, effective L-1-error bounds are also derived for this quadrature formula.", publisher = "Academic Press Inc Elsevier Science, San Diego", journal = "Journal of Approximation Theory", title = "Error bounds of Micchelli-Rivlin quadrature formula for analytic functions", pages = "34-23", volume = "169", doi = "10.1016/j.jat.2013.02.002" }
Pejčev, A.,& Spalević, M.. (2013). Error bounds of Micchelli-Rivlin quadrature formula for analytic functions. in Journal of Approximation Theory Academic Press Inc Elsevier Science, San Diego., 169, 23-34. https://doi.org/10.1016/j.jat.2013.02.002
Pejčev A, Spalević M. Error bounds of Micchelli-Rivlin quadrature formula for analytic functions. in Journal of Approximation Theory. 2013;169:23-34. doi:10.1016/j.jat.2013.02.002 .
Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds of Micchelli-Rivlin quadrature formula for analytic functions" in Journal of Approximation Theory, 169 (2013):23-34, https://doi.org/10.1016/j.jat.2013.02.002 . .