2018/09/26 by R. Orive, Orive, Ramon, Aleksandar V. Pejčev +3
Mathematics · #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1809.10130
openalex publication_date 2018/09/26 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
In this paper, we consider the Gauss quadrature formulae corresponding to\nsome modifications of anyone of the four Chebyshev weights, considered by\nGautschi and Li in citegauli. As it is well known, in the case of analytic\nintegrands, the error of these quadrature formulas can be represented as a\ncontour integral with a complex kernel. We study the kernel, as it is often\nconsidered, on elliptic contours with foci at the points \∓ 1 and such that\nthe sum of semi-axes is \ρ>1, of the mentioned quadrature formulas, and\nderive some error bounds for them. In addition, we obtain, for the first time\nas far as we know, a result about the behavior of the modulus of the\ncorresponding kernels on those ellipses in some cases. Numerical examples\nchecking the accuracy of such error bounds are included.\n