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Optimal quadrature and cubature formulas for singular integrals with Hilbert kernels. (English) Zbl 1085.65026
This paper deals with quadrature and cubature formulas for a singular integral with Hilbert kernel (understood as Cauchy principal value) obtained in terms of discrete analogues of sums of Fourier and Bernstein-Rogosinski. An effective way to estimate the integration errors is proposed. The optimality of these quadrature and cubature formulas in order of accuracy for certain classes of functions is proved.
MSC:
65D32Quadrature and cubature formulas (numerical methods)
41A80Remainders in approximation formulas
41A55Approximate quadratures