Optimization of quadrature formulas for singular Cauchy and Hadamard integrals. (Russian) Zbl 0716.41029

This paper is an ample research work containing new optimalization methods which allow to establish quadrature formulas for singular integrals of Cauchy and Hadamard based on approximation and optimal interpolation. The authors use the polynomial spline functions which together with their derivatives achieve the best approximation with respect to the usual norms and the optimal interpolation. In the approximation formulas, the remainders are estimated through the agency of usual proceedings. The density of calculus and the original quadrature formulas established in this study recommend it to be of use for numerical approximation.
Reviewer: V.Postolică


41A55 Approximate quadratures
41A50 Best approximation, Chebyshev systems
41A05 Interpolation in approximation theory
41A15 Spline approximation