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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 ...
Maximum of the modulus of kernels of Gaussian quadrature formulae for one class of Bernstein-Szego weight functions
(Elsevier Science Inc, New York, 2012)
We continue with the study of 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. The ...
Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials
(Elsevier Science Bv, Amsterdam, 2019)
Generalized averaged Gaussian quadrature rules and truncated variants associated with a nonnegative measure with support on a real open interval {t : a lt t lt b} may have nodes outside this interval, in other words ...
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 ...
Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
(Springer, Dordrecht, 2016)
The need to compute expressions of the form , where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution ...
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 ...
On generalized averaged gaussian formulas. Ii
(Amer Mathematical Soc, Providence, 2017)
Recently, by following the results on characterization of positive quadrature formulae by Peherstorfer, we proposed a new (2l + 1)-point quadrature rule (G) over cap (2l + 1), referred to as a generalized averaged Gaussian ...
A new representation of generalized averaged Gauss quadrature rules
(Elsevier, Amsterdam, 2021)
Gauss quadrature rules associated with a nonnegative measure with support on (part of) the real axis find many applications in Scientific Computing. It is important to be able to estimate the quadrature error when replacing ...
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 ...
Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes
(Springer, Dordrecht, 2016)
The estimation of the error in a quadrature formula is an important problem. A simple and effective procedure for estimating the error of Gaussian quadrature formulas using their extensions with multiple nodes will be ...