| 无限维空间的线性逼近特征 |
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| 引用本文： | 王培,;徐艳艳,;蔡斌畏,;塔实甫拉提.无限维空间的线性逼近特征[J].新疆师范大学学报(自然科学版),2014(2):43-48. |
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| 作者姓名： | 王培 ;徐艳艳 ;蔡斌畏 ;塔实甫拉提 |
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| 作者单位： | [1]西华大学数学与计算机学院,四川成都610039; [2]新疆师范大学数学科学学院,新疆乌鲁木齐830054 |
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| 基金项目： | 国家自然科学基金项目资助（Grant No.61372187） |
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| 摘 要： | 宽度理论由于其与最优算法紧密相连，进而得以蓬勃发展，成为逼近论的重要分支之一。陈广贵和蔡斌畏（2011年）研究了无限维空间在概率框架和平均框架下的非线性逼近特征。文章继续他们的研究，考察了无限维空间在概率和平均框架下的线性逼近特征问题，进而得出了无限维空间在概率框架和平均框架下线性宽度的精确阶。
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| 关 键 词： | 无限维空间 高斯测度 线性( n δ) -宽度 p-平均线性n-宽度 |
The Linear Approximation Characteristic of Infinite-dimension Space |
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| Institution: | WANG Pei, XU Yan-yan, CAI Bin-wei, Tashifulati ( 1. School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan, 610039, China ; 2. The Department of mathematics of Xinjiang Normal University, Urumqi, Xingjiang , 830054, China ) |
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| Abstract: | The theory of width is flourish because of the closely linked with the optimal algorithm. In 2011, Chen guanggui and Cai binwei had studied the nonlinear approximation characteristic of infinite-dimensional space. In this paper, we study the linear approximation characteristic of infinite-dimensional space, and furthermore, we obtain the sharp order of linear widths of infinite-dimensional space in probabilistic setting and average setting. |
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| Keywords: | Infinite-dimensional space Gaussian Measure Linear （ n δ） -widths p-average linear n-widths |
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