| 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),2014,33(3):39-45. |
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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. 新疆师范大学数学系,新疆,乌鲁木齐830053 |
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| 基金项目： | 国家自然科学基金项目资助 |
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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。本文继续他们的研究，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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| WANG Pei,XU Yan-yan,CAI Bin-wei,PU Shifulati.The Linear Approximation Characteristic of Infinite — dimension Space[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2014,33(3):39-45. |
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| Authors: | WANG Pei XU Yan-yan CAI Bin-wei PU Shifulati |
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| Institution: | WANG Pei, XU Yan--yan, CAI Bin--wei, PU Shifulati (1.School of Mathematics and Computer Engineering, X ihua University, Chengdu , 610039 , China; 2.The Department of mathematics of Xinjiang Normal University, Xingjiang , 830053,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--di- mensional 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 proba- bilistic setting and average setting. |
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| Keywords: | Infinite-- dimensional space Gaussian measure Linear （n δ） -- widths p -- average line-ar n -- widths |
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