Paper Info
Title
The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type.
Abstract
We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szegő weight functions consisting of any one of the four Chebyshev weights divided by the polynomial . For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ∓ 1 and sum of semi-axes > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. , 99–127, ).
Year
DOI
Venue
2018
https://doi.org/10.1007/s11075-017-0351-8
Numerical Algorithms
Keywords
Field
DocType
Gauss-Kronrod quadrature formulae,Bernstein-Szegő weight functions,Contour integral representation,Remainder term for analytic functions,Error bound,65D32
Gauss–Kronrod quadrature formula,Discrete mathematics,Mathematical optimization,Gauss,Polynomial,Mathematical analysis,Tanh-sinh quadrature,Clenshaw–Curtis quadrature,Chebyshev filter,Quadrature (mathematics),Ellipse,Mathematics
Journal
Volume
Issue
ISSN
77
4
1017-1398
Citations 
PageRank 
References 
0
0.34
7
Authors
3
Name
Order
Citations
PageRank
Dusan Lj. Djukic131.46
Aleksandar V. Pejčev2103.13
Miodrag M. Spalevic3519.97