共查询到20条相似文献,搜索用时 15 毫秒
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Francisco-Javier Muñoz-Delgado Victoriano Ramirez-González Paul Sablonnière 《分析论及其应用》1995,11(1):62-71
In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials
up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities
and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about
the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained.
This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107 相似文献
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Paulina Pych-Taberska 《Georgian Mathematical Journal》1994,1(5):523-536
In [10], for continuous functionsf from the domain of certain discrete operatorsL n the inequalities are proved concerning the modulus of continuity ofL nf. Here we present analogues of the results obtained for the Durrmeyer-type modification $\tilde L_n $ ofL n. Moreover, we give the estimates of the rate of convergence of $\tilde L_n f$ in Hölder-type norms 相似文献
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J. T. Marti 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1971,22(5):991-996
Zusammenfassung Für eine sehr allgemeine Klasse von Funktionen, die eine kompakte TeilmengeX eines BanachraumesE stetig inE abbilden, wird gezeigt, dass sich jede dieser Funktionen aufX beliebig genau gleichmässig durch entartete Polynomoperatoren approximieren lässt. 相似文献
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For a certain class of discrete approximation operators Bnf defined on an interval I and including, e.g., the Bernstein polynomials, we prove that for all f ε C(I), the ordinary moduli of continuity of Bnf and f satisfy ω(Bnf; h) cω(f; h), N = 1,2,…, 0 < h < ∞, with a universal constant c > 0. A similar result is shown to hold for a different modulus of continuity which is suitable for functions of polynomial growth on unbounded intervals. Some special operators are discussed in this connection. 相似文献
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The problem of approximation in the space of bounded linear operators ? (E;G) between normed spaces E and G by compact operators has been extensively studied in the last few years. Recently Deutsch, Mach and Saatkamp ([2]) have considered the problem of approximating elements of ?(E;G) by the subset K N(E;G) of operators whose range is at most N dimensional. We consider in this paper the problem of approximating operators (not necessarily linear) beteen normed spaces E and G by continuous homogeneous polynomials, and in particular by such polynomials which have finite-dimensional range. 相似文献
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** Email: L.Boulton{at}ma.hw.ac.uk
We establish sufficient conditions for approximation of discreteeigenvalues of self-adjoint operators in the second-order projectionmethod suggested recently in Levitin & Shargorodsky (2004,Spectral pollution and second order relative spectra for self-adjointoperators. IMA J. Numer. Anal., 24, 393416). We findfairly explicit estimates for the eigenvalue error and studyin detail two concrete model examples. Our results show thatsecond-order projection strategies not only are universallypollution free but also achieve approximation under naturalconditions on the discretising basis. 相似文献
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A saturation theorem and an asymptotic theorem are proved for an optimal, discrete, positive algebraic polynomial operator. The operator is based on the Gauss-Legendre quadrature formula. 相似文献
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R. K. Vasil'ev 《Mathematical Notes》1973,13(3):274-280
It is proved that at almost all points the order of approximation, even of one of the functions 1, cos x,sin x by means of a sequence of linear positive polynomial operators having uniformly bounded norms, is not higher than 1/n2. Refinements of this result are given for operators of convolution type.Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 457–468, March, 1973.In conclusion the author expresses thanks to P. P. Korovkin for posing the problem. 相似文献
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Lothar Reichel 《BIT Numerical Mathematics》1986,26(3):349-368
The discrete least squares method is convenient for computing polynomial approximations to functions. We investigate the possibility of using this method to obtain polynomial approximants good in the uniform norm, and find that for a given set ofm nodes, the degreen of the approximating polynomial should be selected so that there is a subset ofn+1 nodes which are close ton+1 Fejér points for the curve. Numerical examples are presented.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. 相似文献
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In the paper, the uniform approximation of a circle arc (or a whole circle) by a parametric polynomial curve is considered. The approximant is obtained in a closed form. It depends on a parameter that should satisfy a particular equation, and it takes only a couple of tangent method steps to compute it. For low degree curves, the parameter is provided exactly. The distance between a circle arc and its approximant asymptotically decreases faster than exponentially as a function of polynomial degree. Additionally, it is shown that the approximant could be applied for a fast evaluation of trigonometric functions too. 相似文献
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Prof. Dany Leviatan 《Mathematische Zeitschrift》1972,124(3):208-212
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Ali Aral Hatice Gül İnce İlarslan Gülen Başcanbaz Tunca 《Mathematical Methods in the Applied Sciences》2016,39(18):5140-5148
The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya‐type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in 1 . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Charles A. Micchelli Jianzhong Wang Yi Wang 《Advances in Computational Mathematics》2013,38(3):601-622
In this paper we provide information about the asymptotic properties of polynomial filters which approximate the ideal filter. In particular, we study this problem in the special case of polynomial halfband filters. Specifically we estimate the error between a polynomial filter and an ideal filter and show that the error decays exponentially fast. For the special case of polynomial halfband filters, our n-th root asymptotic error estimates are sharp. 相似文献
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Marc-Olivier Gebuhrer Ryszard Szwarc 《Proceedings of the American Mathematical Society》1999,127(6):1705-1709
Let be a discrete polynomial hypergoup on with Plancherel measure If the hypergroup is symmetric, the set of characters can be identified with a compact subset of the real line which contains the support of We show that the lower and upper bounds of and coincide. In particular, the trivial character belongs to the support of the Plancherel measure.
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