Abstract
We propose an algorithm for construction of quadrature formulas for linear operators acting on periodic functions. For analytic functions, the order of accuracy of quadrature formulas grows unboundedly with the growth of the number of the grid nodes. Within rather general restrictions on the kernels of linear operators, an exponential estimate of a quadrature formula is proved. To exemplify, we find quadrature formulas for the calculation of integral operators with logarithmic singularities which are used in the boundary element method to obtain overconvergent numerical schemes for solution of boundary value problems for harmonic and biharmonic equations on the plane.
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