Optimal quadrature formulas in the sense of Sard

Abstract

This paper studies the problem of construction of optimal quadrature for- mulas in the sense of Sard in the W (m,m−1) 2 (0,1) space. Using the Sobolev's method we obtain new optimal quadrature formulas of such type for N +1 ≥ m, where N +1 is the number of the nodes. Moreover, explicit formulas of the optimal coefficients are obtained. We investigate the order of convergence of the optimal formula for m = 1

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