| GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS |
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| 引用本文： | S.G. Gal,J. Szabados. GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS[J]. 分析论及其应用, 2003, 19(3): 193-208. DOI: 10.1007/BF02835279 |
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| 作者姓名： | S.G. Gal J. Szabados |
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| 作者单位： | Deptartment of Mathematic University of Oradea，Alfréd Rényi Institute of Mathematic Hungarian Academy of Sciences Str.Armatei Komane 53700 Oradea Romani，P.O.Box 127，H-1364 Budapest Haungar |
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| 摘 要： | 1 IntroductionIn the case when Pn(f,x) represents the univariate interpolation polynomial of Her-mite-Fejér based on Chebyshev nodesof the firstkind or the univariate interpolation polyno-mials of Lagrange based on Chebyshev nodes of the second kind and± 1 ,or the univariaterational Shepard operators,the following result of partial preservation of global smoothnessis proved in[4] :If f∈Lip M(α;[-1 ,1 ] ) ,0 <α≤ 1 ,then there existsβ=β(α) <α and M′>such thatω(Pn(f ) ;h)≤ M′h…
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| 关 键 词： | 二元插值法 球形光滑性 单变量问题 节点 埃尔米特多项式 拉格朗日多项式 |
| 收稿时间： | 2003-04-08 |
Global smoothness preservation by bivariate interpolation operators |
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| S. G. Gal,J. Szabados. Global smoothness preservation by bivariate interpolation operators[J]. Analysis in Theory and Applications, 2003, 19(3): 193-208. DOI: 10.1007/BF02835279 |
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| Authors: | S. G. Gal J. Szabados |
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| Affiliation: | (1) Department of Mathematics, University of Oradea, Str. Armatei Komane 5, 3700 Oradea, Romania;(2) Alfréd Rényi Institute of Mathematics, Hungarian Academy of Science, P. O. Box 127, H-1364 Budapest, Haungary |
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| Abstract: | Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity. |
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| Keywords: | bivariate interpolation polynomials and operators bivariate moduli of continuity global smoothness preservation |
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