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I.J. Schoenberg, On monosplines of least square deviation and best quadrature formulae II. SIAM J. Numer. Anal. v.3, no. 2 (1966) 321-328.

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Article

Optimal Quadrature Formulas with Derivative in the Space L2(m)(0,1)

1Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan


American Journal of Numerical Analysis. 2014, Vol. 2 No. 4, 115-127
DOI: 10.12691/ajna-2-4-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Abdullo R. Hayotov, Farhod A. Nuraliev, Kholmat M. Shadimetov. Optimal Quadrature Formulas with Derivative in the Space L2(m)(0,1). American Journal of Numerical Analysis. 2014; 2(4):115-127. doi: 10.12691/ajna-2-4-4.

Correspondence to: Abdullo  R. Hayotov, Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan. Email: hayotov@mail.ru

Abstract

This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number and for any using S.L. Sobolev method which is based on discrete analogue of the differential operator. In particular, for m=2,3 optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from m=4 new optimal quadrature formulas are obtained.

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