Article ID Journal Published Year Pages File Type
4641041 Journal of Computational and Applied Mathematics 2009 6 Pages PDF
Abstract

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 the points ±1 and the sum of semi-axes ϱ>1ϱ>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod’s method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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