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【期刊论文】Approximation properties of Gamma operators✩
曾晓明, Xiao-Ming Zeng
J. Math. Anal. Appl. 311(2005)389-401,-0001,():
-1年11月30日
In this paper the approximation properties of Gamma operators Gn are studied to the locally bounded functions and the absolutely continuous functions, respectively. Firstly, in Section 2 of the paper a quantitative form of the central limit theorem in probability theory is used to derive an asymptotic formula on approximation of Gamma operators Gn for sign function. And then, this asymptotic formula combining with a metric form Ωx(f, λ) is used to derive an asymptotic estimate on the rate of convergence of Gamma operators Gn for the locally bounded functions. Next, in Section 3 of the paper the optimal estimate on the first order absolute moment of the Gamma operators Gn(|t −x|, x) is obtained by direct computations. And then, this estimate and Bojanic-Khan-Cheng's method combining with analysis techniques are used to derive an asymptotically optimal estimate on the rate of convergence of Gamma operators Gn for the absolutely continuous functions.
Approximation properties, Locally bounded functions, Absolutely continuous functions, Gamma operators, Probabilistic methods
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【期刊论文】Computational formula of depth for Catmull-Clark subdivision surfaces
曾晓明, Xiao-Ming Zeng∗, X.J. Chen
Journal of Computational and Applied Mathematics 195(2006)252-262,-0001,():
-1年11月30日
In this paper, by introducing the concept of neighbor points and using the first-order difference of control points of Catmull-Clark surfaces, we obtain the rate of convergence of control meshes of Catmull-Clark surface. By the result of convergence we derive a computational formula of subdivision depth for Catmull-Clark surfaces.
Subdivision, Catmull-Clark surfaces, Rate of convergence, Control points
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【期刊论文】On the Rates of Approximation of Bernstein Type Operators
曾晓明, Xiao-Ming Zeng, and Fuhua (Frank) Cheng
Journal of Approximation Theory 109, 242-256(2001),-0001,():
-1年11月30日
Asymptotic behavior of two Bernstein-type operators is studied in this paper. In the first case, the rate of convergence of a Bernstein operator for a bounded function f is studied at points x where f (x+) and f (x-) exist. In the second case, the rate of convergence of a Szasz operator for a function f whose derivative is of bounded variation is studied at points X where f (x+) and f (x-) exist. Estimates of the rate of convergence are obtained for both cases and the estimates are the best possible for continuous points.
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