Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions
arXiv:1802.026353 citationsh-index: 14
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Provides theoretical error bounds for a specialized numerical integration method, but the contribution is incremental for researchers in approximation theory.
The paper provides three effective error bounds for quadrature formulas with multiple nodes, generalizing the Micchelli-Rivlin formula for analytic functions in confocal ellipses, and includes a numerical example.
Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.