| 由Fourier系数确定的函数类的最佳m-项单边逼近渐近估计 |
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| 引用本文： | 李仁所,刘永平. 由Fourier系数确定的函数类的最佳m-项单边逼近渐近估计[J]. 数学进展, 2008, 37(2): 211-221 |
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| 作者姓名： | 李仁所 刘永平 |
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| 作者单位： | 1. 山东农业大学数学系,泰安,山东,271018
2. 北京师范大学数学科学学院,北京,100875 |
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| 基金项目： | 国家自然科学基金 , 北京师范大学"985工程"项目 , 北京市自然科学基金 |
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| 摘 要： | 结合最佳m项逼近和单边逼近的思想引进所谓最佳m项单边逼近的概念,给出由Fourier系数确定的光滑函数类通过三角函数系在Lp(1≤P≤∞)的最佳m-项单边逼近渐近估计以及m-项类贪婪单边逼近结果.
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| 关 键 词： | 最佳m项逼近 单边逼近 三角函数系 贪婪逼近算法 best m-term approximation one-sided approximation trigonometric function system greedy approximation algorithm Fourier Coefficients 系数确定 光滑函数类 最佳 单边逼近 渐近估计 Classes Function Approximation Best results classes Fourier coefficients function system norm asymptotic estimates nonlinear introduced |
| 文章编号： | 1000-0917(2008)02-0211-11 |
| 修稿时间： | 2005-11-22 |
The Asymptotic Estimations of Best m-term One-sided Approximation of Function Classes Determined by Fourier Coefficients |
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| LI Rensuo,LIU Yongping. The Asymptotic Estimations of Best m-term One-sided Approximation of Function Classes Determined by Fourier Coefficients[J]. Advances in Mathematics(China), 2008, 37(2): 211-221 |
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| Authors: | LI Rensuo LIU Yongping |
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| Abstract: | In this Paper a new kind of approximation method,called non-linear m-term onesided approximation,is introduced by combining the non-linear best m-term approximation with the one-sided approximation.With this new kind of approximation method,asymptotic estimates of nonlinear best m-term one-sided approximation,given by the trigonometric function system under the norm Lp(1≤P≤∞)of function classes determined by Fourier coefficients,and corresponding m-term greedy-liked one-sided approximation results are given. |
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| Keywords: | best m-term approximation one-sided approximation trigonometric function system greedy approximation algorithm |
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