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Error estimates for Gaussian quadratures of analytic functions
(Elsevier Science Bv, Amsterdam, 2009)
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at ...
Error bounds of certain Gaussian quadrature formulae
(Elsevier Science Bv, Amsterdam, 2010)
We study the kernel of the remainder term of Gauss quadrature rules for analytic functions with respect to one class of Bernstein-Szego weight functions. The location on the elliptic contours where the modulus of the kernel ...
Error bounds of the Micchelli-Sharma quadrature formula for analytic functions
(Elsevier Science Bv, Amsterdam, 2014)
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 ...
Truncated generalized averaged Gauss quadrature rules
(Elsevier Science Bv, Amsterdam, 2016)
Generalized averaged Gaussian quadrature formulas may yield higher accuracy than Gauss quadrature formulas that use the same moment information. This makes them attractive to use when moments or modified moments are ...
Error estimates of anti-Gaussian quadrature formulae
(Elsevier Science Bv, Amsterdam, 2012)
Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the ...
Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind
(Elsevier Science Bv, Amsterdam, 2019)
Generalized averaged Gaussian quadrature rules associated with some measure, and truncated variants of these rules, can be used to estimate the error in Gaussian quadrature rules. However, the former quadrature rules may ...
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind
(Elsevier, Amsterdam, 2021)
It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a ...