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ON THE order of approximation FOR THE RATIONAL INTERPOLATION TO |x|

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approximation Theory and Its Applications 2002年第2期18卷 58-64页

作者： Han Xuli(Central South University, China) Central South University China

The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are estimated. The result illustrates the general quality of approximation in a different way. For thespecial case where the interpolation nodes are Xi=(i/n)r(i = 1,2,'' ,n;r>0) . it is proved that the exact order of approximation is O(1/n),O(1/nlogn) and O(1/nr), respectively, corresponding to Ol.

关键词： RATIONAL INTERPOLATION order of approximation rational interpolation approximation error

Jackson type theorems on complex curves

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Science China Mathematics 2009年第3期52卷 493-506页

作者： TU TianLiang Deptartment of Mathematics and Informatics, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, China Deptartment of Mathematics and Informatics North China Institute of Water Conservancy and Hydroelectric Power Zhengzhou China

Let Γ be a closed smooth Jordan curve in the complex plane. In this paper, with the help of a class of fundamental functions of Hermite interpolation, the author introduces a continuous function interpolation which uniformly approximates to f(z) ∈ C(Γ ) with the same order of approximation as that in Jackson Theorem 1 on real interval [1, 1]. The accuracy of the order of approximation is proved. Using the method different from the early works, the author studies simultaneous approximation to function and its derivatives and the desired results analogues to that in Jackson Theorem 2 on real interval [1, 1] are obtained.

关键词： complex curves interpolation uniform approximation order of approximation 30E05 30E10 41A05 41A25 41A28

COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJR POINTS ON A CURVE

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Acta Mathematica Scientia 2012年第2期32卷 441-454页

作者：涂天亮莫烔 Department of Mathematics and Informatics North China Institute of Water Conservancy and Hydroelectric PowerBeihuan Roal No.36Zhengzhou 450011China Department of Physics Zhengzhou University

The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊）＋ Sk are also proved in this article.

关键词： Disturbed Fejer points complex interpolation order of approximation closed Jordan curve uniform convergence

M_n(~R) (a_n, f, x) Apporximation in L_p[0, l]

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Chinese Quarterly Journal of Mathematics 1992年第3期7卷 95-100页

作者：陈广荣刘吉善河北机电学院大连水产学院 116023

Generalized Bernstein-Kantorovich polynomials M_n^((k))(a_n, f, x) were introduced in the paper and their order of approximation were estimated in the L_p[0, 1]-spaces.

关键词： estimate order of approximation

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|x|在Newman结点组的有理插值

高等学校计算数学学报 2016年第4期38卷 367-374页

作者：张慧明李建俊河北地质大学数理学院河北师范大学附属民族学院

1引言一个世纪以前,Bernstein[1]最早研究|x|的逼近问题.他用n次代数多项式逼近|x|,得到逼近阶为En(|x|)=O(1/n),且不能改善.半个世纪后的1964年,Newman[2]构造有理函数

关键词： Newman nodes Newman-type rational operators Newman inequality rational interpolation order of approximation

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|x|的有理插值

高等学校计算数学学报 2016年第1期38卷 52-59页

作者：张慧明段生贵李建俊辛玉东石家庄经济学院数理学院河北师范大学附属民族学院

The asymptotic property of approximation to |x| is *** is proved that,if increase nodes near zero,the order of approximation for the Newman-type rational interpolation to |x| at the second kind of Chebyshev nodes is O(1/(n~2logn)).And get a very important conclusion:increases nodes in the near zero can improve the approximation order of the original.

关键词： Chebyshev nodes of the second kind rational interpolation Newman-type rational operators order of approximation