Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4641041 | Journal of Computational and Applied Mathematics | 2009 | 6 Pages |
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
Authors
Gradimir V. Milovanović, Miodrag M. Spalević, Miroslav S. Pranić,