共查询到17条相似文献,搜索用时 125 毫秒
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本文引入了一种修正的积分型Shepard算子,建立了相应的Jackson型定理,并通过建立Bernstein型不等式,给出了算子在L[0,1]p空间中一种新的逼近阶刻画的等价形式,得到了逼近的逆定理. 相似文献
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本文研究一类多元Gauss-Weierstrass算子的线性组合加Jacobi型权逼近的性质,利用加权矩量不等式及加权K-泛函、光滑模等工具,建立了这类算子在Lp(1≤p≤∞)空间的正、逆定理和逼近阶的特征刻划. 相似文献
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对于局部有界函数的积分型Szász-Bézier算子的逼近估计 总被引:1,自引:0,他引:1
引入一种积分型的Szász-Bézier算子,并研究其逼近性质,得到了此类算子对局部有界函数的逼近阶估计公式. 相似文献
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Post-Widder算子线性组合加Jacobi权的Lp同时逼近 总被引:1,自引:0,他引:1
赵德钧 《纯粹数学与应用数学》2000,16(4):33-40
给出了Post-Widder算子线性组合加Jacobi权的Lp同时逼近的正、逆定理和逼近阶的特征刻划. 相似文献
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引入一种积分型的 Szász- Bézier算子 ,并研究其逼近性质 ,得到了此类算子对局部有界函数的逼近阶估计公式 相似文献
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Dan Sheng Yu 《数学学报(英文版)》2013,29(10):2013-2026
In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals. 相似文献
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Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory. In this paper, we aim at constructing deep neural networks with three hidden layers using a sigmoidal activation function to approximate smooth and sparse functions. Specifically, we prove that the constructed deep nets with controllable magnitude of free parameters can reach the optimal approximation rate in approximating both smooth and sparse functions. In particular, we prove that neural networks with three hidden layers can avoid the phenomenon of saturation, i.e., the phenomenon that for some neural network architectures, the approximation rate stops improving for functions of very high smoothness. 相似文献
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修正的Bernstein-Durrmeyer算子的同时逼近 总被引:1,自引:0,他引:1
本文的目的是证明修正的Bernstein-Durrmeyer算子同时逼近的正逆定理,在点态意义下,我们得到了一个同时逼近的等价特征刻画。 相似文献
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Lin Sen XIE Zhong Rui SHI 《数学学报(英文版)》2007,23(5):935-944
In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. 相似文献