The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions
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2016
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We consider the Gauss-Radau quadrature formulae integral(1)(-1) f(t)w(t)dt = (n)Sigma(nu=1) lambda(nu)f(tau(nu)) + lambda(n+1) f(c) + R-n(f), with or , for the Bernstein-SzegA weight functions consisting of anyone of the four Chebyshev weights divided by the polynomial . 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 and a sum of semi-axes , for the given 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 error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed recently by Notaris (Math Comp 10.1090/mcom/2944, 2015).
Извор:
Numerische Mathematik, 2016, 133, 1, 177-201Издавач:
- Springer Heidelberg, Heidelberg
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1007/s00211-015-0740-7
ISSN: 0029-599X
WoS: 000372614200006
Scopus: 2-s2.0-84931090262
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Институција/група
Mašinski fakultetTY - JOUR AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2409 AB - We consider the Gauss-Radau quadrature formulae integral(1)(-1) f(t)w(t)dt = (n)Sigma(nu=1) lambda(nu)f(tau(nu)) + lambda(n+1) f(c) + R-n(f), with or , for the Bernstein-SzegA weight functions consisting of anyone of the four Chebyshev weights divided by the polynomial . 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 and a sum of semi-axes , for the given 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 error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed recently by Notaris (Math Comp 10.1090/mcom/2944, 2015). PB - Springer Heidelberg, Heidelberg T2 - Numerische Mathematik T1 - The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions EP - 201 IS - 1 SP - 177 VL - 133 DO - 10.1007/s00211-015-0740-7 ER -
@article{ author = "Pejčev, Aleksandar and Spalević, Miodrag", year = "2016", abstract = "We consider the Gauss-Radau quadrature formulae integral(1)(-1) f(t)w(t)dt = (n)Sigma(nu=1) lambda(nu)f(tau(nu)) + lambda(n+1) f(c) + R-n(f), with or , for the Bernstein-SzegA weight functions consisting of anyone of the four Chebyshev weights divided by the polynomial . 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 and a sum of semi-axes , for the given 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 error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed recently by Notaris (Math Comp 10.1090/mcom/2944, 2015).", publisher = "Springer Heidelberg, Heidelberg", journal = "Numerische Mathematik", title = "The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions", pages = "201-177", number = "1", volume = "133", doi = "10.1007/s00211-015-0740-7" }
Pejčev, A.,& Spalević, M.. (2016). The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions. in Numerische Mathematik Springer Heidelberg, Heidelberg., 133(1), 177-201. https://doi.org/10.1007/s00211-015-0740-7
Pejčev A, Spalević M. The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions. in Numerische Mathematik. 2016;133(1):177-201. doi:10.1007/s00211-015-0740-7 .
Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of Gauss-Radau quadrature formulae with Bernstein-SzegA weight functions" in Numerische Mathematik, 133, no. 1 (2016):177-201, https://doi.org/10.1007/s00211-015-0740-7 . .