Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights
Само за регистроване кориснике
2013
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The kernels K-n(z) in the remainder terms R-n(f) of the Gaussian quadrature formulae for analytic functions f inside elliptical contours with foci at -/+ 1 and a sum of semi- axes rho > 1, when the weight function w is of Bernstein-Szego type w(t) equivalent to w gamma((-1/2,1/2)) (t) = root 1+t/1-t.1/1-4 gamma/(1+gamma)(2) t(2), t is an element of (-1,1), gamma is an element of (-1,0), are studied. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with the positive real semi-axis. This leads to effective error bounds of the corresponding Gauss quadratures. The quality of the derived bounds is analyzed by a comparison with other error bounds intended for the same class of integrands. In part our analysis is based on the well-known Cardano formulas, which are not very popular among mathematicians.
Кључне речи:
modulus / Maximum / kernel / Gaussian quadrature formula / Bernstein-Szego weight functionИзвор:
Mathematics of Computation, 2013, 82, 282, 1037-1056Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1090/S0025-5718-2012-02667-6
ISSN: 0025-5718
WoS: 000326287500017
Scopus: 2-s2.0-84873271643
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Институција/група
Mašinski fakultetTY - JOUR AU - Spalević, Miodrag PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1738 AB - The kernels K-n(z) in the remainder terms R-n(f) of the Gaussian quadrature formulae for analytic functions f inside elliptical contours with foci at -/+ 1 and a sum of semi- axes rho > 1, when the weight function w is of Bernstein-Szego type w(t) equivalent to w gamma((-1/2,1/2)) (t) = root 1+t/1-t.1/1-4 gamma/(1+gamma)(2) t(2), t is an element of (-1,1), gamma is an element of (-1,0), are studied. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with the positive real semi-axis. This leads to effective error bounds of the corresponding Gauss quadratures. The quality of the derived bounds is analyzed by a comparison with other error bounds intended for the same class of integrands. In part our analysis is based on the well-known Cardano formulas, which are not very popular among mathematicians. T2 - Mathematics of Computation T1 - Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights EP - 1056 IS - 282 SP - 1037 VL - 82 DO - 10.1090/S0025-5718-2012-02667-6 ER -
@article{ author = "Spalević, Miodrag", year = "2013", abstract = "The kernels K-n(z) in the remainder terms R-n(f) of the Gaussian quadrature formulae for analytic functions f inside elliptical contours with foci at -/+ 1 and a sum of semi- axes rho > 1, when the weight function w is of Bernstein-Szego type w(t) equivalent to w gamma((-1/2,1/2)) (t) = root 1+t/1-t.1/1-4 gamma/(1+gamma)(2) t(2), t is an element of (-1,1), gamma is an element of (-1,0), are studied. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with the positive real semi-axis. This leads to effective error bounds of the corresponding Gauss quadratures. The quality of the derived bounds is analyzed by a comparison with other error bounds intended for the same class of integrands. In part our analysis is based on the well-known Cardano formulas, which are not very popular among mathematicians.", journal = "Mathematics of Computation", title = "Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights", pages = "1056-1037", number = "282", volume = "82", doi = "10.1090/S0025-5718-2012-02667-6" }
Spalević, M.. (2013). Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights. in Mathematics of Computation, 82(282), 1037-1056. https://doi.org/10.1090/S0025-5718-2012-02667-6
Spalević M. Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights. in Mathematics of Computation. 2013;82(282):1037-1056. doi:10.1090/S0025-5718-2012-02667-6 .
Spalević, Miodrag, "Error bounds of gaussian quadrature formulae for one class of bernstein-szego weights" in Mathematics of Computation, 82, no. 282 (2013):1037-1056, https://doi.org/10.1090/S0025-5718-2012-02667-6 . .