Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631396 | Applied Mathematics and Computation | 2012 | 11 Pages |
Abstract
We continue with the study of the kernels Kn(z) in the remainder terms Rn(f) of the Gaussian quadrature formulae for analytic functions f inside elliptical contours with foci at â1 and a sum of semi-axes Ï > 1. The weight function w of Bernstein-SzegÅ type here isw(t)â¡wγ(-1/2)(t)=11-t2·1-4γ(1+γ)2t2-1,tâ(-1,1),γâ(-1,0).Sufficient conditions are found ensuring that the kernel attains its maximum absolute value at the intersection point of the contour with either the real or the imaginary axis. This leads to effective error bounds of the corresponding Gauss quadratures. The quality of the derived bounds is demonstrated by a comparison with other error bounds intended for the same class of integrands.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Miodrag M. SpaleviÄ, Miroslav S. PraniÄ, Aleksandar V. PejÄev,