On the composite Bernstein type quadrature formula

Author:

Bărbosu Dan,Miclăuş Dan

Abstract

Considering a given function \(f\in C[0,1]\), the interval \([0,1]\) is divided in \(m\) equally spaced subintervals \(\left[\tfrac{k-1}{m},\tfrac{k}{m}\right]\), \(k=\overline{1,m}\). On each of such type of interval the Bernstein approximation formula is applied and a corresponding Bernstein type quadrature formula is obtained. Making the sum of mentioned quadrature formulas, the composite Bernstein type quadrature formula is obtained.

Publisher

Academia Romana Filiala Cluj

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis,Mathematics (miscellaneous)

Reference6 articles.

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3. Popoviciu, T., Sur le rest dans certains formules lineaires d'approximation de l'analyse, Mathematica I, 24, pp. 95-142, 1959.

4. Stancu, D. D., Quadrature formulas constructed by using certain linear positive operators, Numerical Integration (Proc. Conf. Math. Res. Inst. Oberwolffach) (Basel) (G. Hammerlin, ed.), Birkhäuser, pp. 241-251, 1982.

5. Stancu, D. D. and Vernescu, A., On some remarkable positive polynomial operators of approximation, Rev. Anal. Numér. Th eor. Approx., 28, pp. 85-95, 1999, http://ictp.acad.ro/jnaat/journal/article/view/1999-vol28-no1-art8

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sur la suite des opérateurs Bernstein composés;Journal of Numerical Analysis and Approximation Theory;2013-08-01

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