Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems
A combination of two approaches to the derivative-free representation of the remainder term in quadrature formulas is proposed. One of these approaches is based on the contour integral representation with complex kernel function. Another one represents the remainder as a bounded linear functional in an appropriate Hilbert space. The kernel function is estimated by using the method of biorthogonal systems (namely, of Chebyshev type). This scheme is applied to the Clenshaw-Curtis, Pólya and Filippi quadrature formulas. The error bounds for the Gauss-Chebyshev and Lobatto-Chebyshev formulas are illustrated by the series of numerical results obtained within the framework of the discussed method.
scientific article; zbMATH DE number 1419745