共查询到20条相似文献,搜索用时 328 毫秒
1.
George A. Anastassiou 《Mathematical and Computer Modelling》2011,53(5-6):1111-1132
Here we study the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation hyperbolic tangent neural network operators. This approximation is derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its high order derivative. Our operators are defined by using a density function induced by the hyperbolic tangent function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural network is with one hidden layer. 相似文献
2.
In this paper,the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions.Using the modulus of continuity of function as a metric,... 相似文献
3.
Zhengqiu Zhang Kaiyu Liu Li Zhu Yanju Chen 《Journal of Applied Mathematics and Computing》2013,42(1-2):455-468
The aim of this paper is to investigate approximation operators with logarithmic sigmoidal function of a class of two neural networks weights and a class of quasi-interpolation operators. Using these operators as approximation tools, the upper bounds of estimate errors are estimated for approximating continuous functions. 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
6.
Quasi-interpolation of radial basis functions on finite grids is a very useful strategy in approximation theory and its applications. A notable strongpoint of the strategy is to obtain directly the approximants without the need to solve any linear system of equations. For radial basis functions with Gaussian kernel, there have been more studies on the interpolation and quasi-interpolation on infinite grids. This paper investigates the approximation by quasi-interpolation operators with Gaussian kernel on the compact interval. The approximation errors for two classes of function with compact support sets are estimated. Furthermore, the approximation errors of derivatives of the approximants to the corresponding derivatives of the approximated functions are estimated. Finally, the numerical experiments are presented to confirm the accuracy of the approximations. 相似文献
7.
首先,引入一种由斜坡函数激发的神经网络算子,建立了其对连续函数逼近的正、逆定理,给出了其本质逼近阶.其次,引入这种神经网络算子的线性组合以提高逼近阶,并且研究了这种组合的同时逼近问题.最后,利用Steklov函数构造了一种新的神经网络算子,建立了其在L~p[a,b]空间逼近的正、逆定理. 相似文献
8.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(9):2262-2266
The power generated by wind turbines changes rapidly because of the continuous fluctuation of wind speed and air density. As a consequence, it can be important to predict the energy production, starting from some basic input parameters. The aim of this paper is to show that a two-hidden layer neural network can represent a useful tool to carefully predict the wind energy output. By using proper experimental data (collected from three wind farm in Southern Italy) in combination with a back propagation learning algorithm, a suitable neural architecture is found, characterized by the hyperbolic tangent transfer function in the first hidden layer and the logarithmic sigmoid transfer function in the second hidden layer. Simulation results are reported, showing that the estimated wind energy values (predicted by the proposed network) are in good agreement with the experimental measured values. 相似文献
9.
In this paper, a family of interpolation neural network operators are introduced. Here, ramp functions as well as sigmoidal functions generated by central B-splines are considered as activation functions. The interpolation properties of these operators are proved, together with a uniform approximation theorem with order, for continuous functions defined on bounded intervals. The relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed. 相似文献
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J. Lyle Noakes 《Advances in Computational Mathematics》1996,5(1):153-161
Neural networks calledtangent networks are constructed by explicit reference to the geometry of a set, and then blended intocascades which approximate characteristic functions of closed balls. In this way some known results about approximation by single hidden layer neural networks are re-proved in a very constructive and geometrical fashion. 相似文献
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《European Journal of Operational Research》1998,105(1):130-142
An artificial neural network (ANN) model for economic analysis of risky projects is presented in this paper. Outputs of conventional simulation models are used as neural network training inputs. The neural network model is then used to predict the potential returns from an investment project having stochastic parameters. The nondeterministic aspects of the project include the initial investment, the magnitude of the rate of return, and the investment period. Backpropagation method is used in the neural network modeling. Sigmoid and hyperbolic tangent functions are used in the learning aspect of the system. Analysis of the outputs of the neural network model indicates that more predictive capability can be achieved by coupling conventional simulation with neural network approaches. The trained network was able to predict simulation output based on the input values with very good accuracy for conditions not in its training set. This allowed an analysis of the future performance of the investment project without having to run additional expensive and time-consuming simulation experiments. 相似文献
14.
In the present paper, we find that the Bemstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallee properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt. 相似文献
15.
In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported radial kernels, and use them to approximate Sobolev space functions with optimal convergence order. These kernels can be simply constructed and readily applied to practical problems. The results show that the approximation power depends on the precision of the sampling instrument and the density of the available data. 相似文献
16.
Recently, Li [16] introduced three kinds of single-hidden layer feed-forward
neural networks with optimized piecewise linear activation functions and fixed
weights, and obtained the upper and lower bound estimations on the approximation
accuracy of the FNNs, for continuous function defined on bounded intervals. In the
present paper, we point out that there are some errors both in the definitions of the
FNNs and in the proof of the upper estimations in [16]. By using new methods, we
also give right approximation rate estimations of the approximation by Li’s neural
networks. 相似文献
17.
Zhixiang Chen 《Applied mathematics and computation》2010,217(2):725-734
This paper investigates the global errors which result when the method of approximate approximations is applied to a function defined on a compact interval. By extending the functions to a wider interval, we are able to introduce modified forms of the quasi-interpolant operators. Using these operators as approximation tools, we estimate upper bounds on the errors in terms of a uniform norm. We consider only continuous and differentiable functions. A similar problem is solved for the two-dimensional case. 相似文献
18.
V. I. Bilenko 《Journal of Mathematical Sciences》1993,63(5):561-567
We describe a numerical-analytical algorithm to solve the boundary-value problem for the integrodifferential equation of particle transport in a plane homogeneous medium. The general scheme of approximate solution of this problem is based on its reduction to the solution of some integral equation by summator operators of function approximation theory. Solvability conditions are established for the approximate equations and the algorithm errors are estimated. Working formulas are presented for the algorithm implemented in the form of a computer program. The summator operators in this algorithm are the algebraic interpolation operators with nodes at the extremal points of Chebyshev polynomials of first kind.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 69–76, 1987. 相似文献
19.
Masato Tanaka Takashi Sasagawa Ryuji Omote Masaki Fujikawa Daniel Balzani Jörg Schröder 《PAMM》2014,14(1):429-430
Many materials as e.g. engineering rubbers, polymers and soft biological tissues are often described by hyperelastic strain energy functions. For their finite element implementation the stresses and consistent tangent moduli are required and obtained mainly in terms of the first and second derivative of the strain energy function. Depending on its mathematical complexity in particular for anisotropic media the analytic derivatives may be expensive to be calculated or implemented. Then numerical approaches may be a useful alternative reducing the development time. Often-used classical finite difference schemes are however quite sensitive with respect to perturbation values and they result in a poor accuracy. The complex-step derivative approximation does never suffer from round-off errors, cf. [1], [2], but it can only provide first derivatives. A method which also provides higher order derivatives is based on hyper dual numbers [3]. This method is independent on the choice of perturbation values and does thus neither suffer from round-off errors nor from approximation errors. Therefore, here we make use of hyper dual numbers and propose a numerical scheme for the calculation of stresses and tangent moduli which are almost identical to the analytic ones. Its uncomplicated implementation and accuracy is illustrated by some representative numerical examples. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials,
and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous
functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic
polynomial. 相似文献