ERROR ESTIMATES OF GAUSSIAN QUADRATURE FORMULAE WITH THE THIRD CLASS OF BERNSTEIN-SZEGO WEIGHTS

Applicable Analysis and Discrete Mathematics

article

Aleksandar Pejčev¹ 

[1] Department of Mathematics, University of Beograd, Faculty of Mechanical Engineering

关键词: error bound;    elliptic contour;    Gauss quadrature;    remainder term;    analytic function;   

DOI  :  10.2298/AADM1702451P

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

For analytic functions we study the remainder terms of Gauss quadraturerules with respect to Bernstein-Szeg˝o weight functionsw(t) = wα,β,δ(t) =r1 + t1 − tβ(β − 2α)t2 + 2δ(β − α)t + α2 + δ2, t ∈ (−1, 1),where 0 < α < β, β 6= 2α, |δ| < β−α, and whose denominator is an arbitrarypolynomial of exact degree 2 that remains positive on [−1, 1]. The subcaseα = 1, β = 2/(1 + γ), −1 < γ < 0 and δ = 0 has been considered recently byM. M. Spalevi´c, Error bounds of Gaussian quadrature formulae for one classof Bernstein-Szeg˝o weights, Math. Comp., 82 (2013), 1037-1056.

【 授权许可】

Unknown