Paper Info
Title
Error bounds of the Micchelli-Sharma quadrature formula for analytic functions.
Abstract
Micchelli and Sharma constructed in their paper [On a problem of Turan: multiple node Gaussian quadrature, Rend. Mat. 3 (1983) 529-552] a quadrature formula for the Fourier-Chebyshev coefficients, which has the highest possible precision. 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 a sum of semi-axes @r1, for the quoted quadrature formula. Starting from the explicit expression of the kernel, we determine the location on the ellipses where the maximum modulus of the kernel is attained, and derive effective error bounds for this quadrature formula. Numerical examples are included.
Year
DOI
Venue
2014
10.1016/j.cam.2013.03.039
J. Computational Applied Mathematics
Keywords
Field
DocType
micchelli-sharma quadrature formula,highest possible precision,quadrature formula,explicit expression,analytic function,maximum modulus,elliptic contour,complex kernel,multiple node gaussian quadrature,derive effective error bound,fourier-chebyshev coefficient,primary
Gauss–Kronrod quadrature formula,Mathematical optimization,Mathematical analysis,Tanh-sinh quadrature,Clenshaw–Curtis quadrature,Gauss–Hermite quadrature,Quadrature domains,Gauss–Jacobi quadrature,Gaussian quadrature,Mathematics,Gauss–Laguerre quadrature
Journal
Volume
ISSN
Citations 
259
0377-0427
2
PageRank 
References 
Authors
0.41
3
2
Name
Order
Citations
PageRank
Aleksandar V. Pejčev1103.13
Miodrag M. Spalevic2519.97