| 非周期神经网络及平移网络在L_w~p中的逼近 |
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| 引用本文： | 王建力,盛宝怀,周颂平.非周期神经网络及平移网络在L_w~p中的逼近[J].数学学报,2003,46(1):65-74. |
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| 作者姓名： | 王建力 盛宝怀 周颂平 |
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| 作者单位： | 1. 宁波大学数学研究所,宁波,315211;绍兴文理学院数学系,绍兴,312000
2. 宁波大学数学研究所,宁波,315211;西南石油学院计算机科学系,南充,637001 |
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| 基金项目： | 国家自然科学基金资助项目(10141001)，宁波市博士基金(02J20102-06)，宁波大学博士后基金资助项目 |
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| 摘 要： | 设s≥d≥1为整数, 1≤p≤+∞,借助于正交多元代数多项式系而构造了一类s维网络算子,并用于逼近Lpw-1,1]s中的函数,给出了逼近的上界以及当此算子为平移网络算子及神经网络算子时的导数型估计.
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| 关 键 词： | 正交系 神经网络 平移网络 逼近 |
| 文章编号： | 0583-1431(2003)01-0065-10 |
| 修稿时间： | 2001年7月5日 |
On Approximation by Non-Periodic Neural and Translation Networks in L~p-w, Spaces |
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| Jian Li WANG.On Approximation by Non-Periodic Neural and Translation Networks in L~p-w, Spaces[J].Acta Mathematica Sinica,2003,46(1):65-74. |
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| Authors: | Jian Li WANG |
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| Institution: | Jian Li WANG(Institute of Mathematics, Ningbo University, Ningbo 315211, P. R. China) (Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, P. R. China)Bao Huai SHENG Song Ping ZHOU(Institute of Mathematics, Ningbo University, Ningbo 315211, P. R. China) (Department of Computer Science, Southwest Institute of Petroleum, Nanchong 637001, P. R. China) |
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| Abstract: | The authors investigate the approximation of non-periodic functions in by a kind of s-dimensional network operator constructed by orthogonal algebraic polynomial. The upper bound of approximation is achieved and, in particular, the upper bound of approximation of the derivatives of the target functions by the corresponding derivatives of the translate and neural network operators is discussed. |
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| Keywords: | Orthogonal series Neural network Translate network Approximation |
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