For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes > 1 for the Chebyshev weight functions of
Some observations on Gauss-Legendre quadrature error estimates for analytic functions
✍ Scribed by Frank G. Lether
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 260 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0377-0427
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For analytic functions the remainder term of Gauss-Radau quadrature formulae 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 > 1 for the Chebyshev weight function of the second kind. Starting f
We consider the problem of integrating a function f : [-1, l] -+ R which has an analytic extension f to an open disk Dr of radius r and center the origin, such that If(z)] 5 1 for any z E d,. The goal of this paper is to study the minimal error among all algorithms which evaluate the integrand at t