Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems

Summary. For analytic functions the remainder term of quadrature rules can be represented as a contour integral with a complex kernel function. From this representation different remainder term estimates involving the kernel are obtained. It is studied in detail how polynomial biorthogonal systems can be applied to derive sharp bounds for the kernel function. It is shown that these bounds are practical to use and can easily be computed. Finally, various numerical examples are presented. Received March 11, 1998 / Revised version January 22, 1999/ Published online November 17, 1999