Is Gauss quadrature optimal for analytic functions?
✍ Scribed by M. A. Kowalski; A. G. Werschulz; H. Woźniakowski
- Publisher
- Springer-Verlag
- Year
- 1985
- Tongue
- English
- Weight
- 424 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0029-599X
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For analytic functions the remainder term of Gauss-Lobatto quadrature rules can be represented as a contour integral with a complex kernel. In this paper the kernel is studied on elliptic contours for the Chebyshev weight functions of the second, third, and fourth kind. Starting from explicit expres
A two-parameter class of refinable functions is considered and Gaussian quadrature rules having these functions as weight functions. A discretization method is described for generating the recursion coefficients of the required orthogonal polynomials. Numerical results are also presented.