【作者】 董锐；

【导师】 王连明；

【作者基本信息】 东北师范大学 ， 电路与系统， 2011， 硕士

【摘要】 函数逼近是函数论中的一个重要组成部分,其在数值计算中的作用是十分重要的。运用神经网络进行函数逼近,为函数逼近的发展提供了一条新的思路。用神经网络作函数的逼近有许多优点:首先,它提供了一个标准的逼近结构及逼近工具,这个工具可以随着隐层个数改变来达到任意精度;其次,有标准的学习算法用以确定逼近函数的参数,并且这一过程是拟人的,即很好地模拟了人的学习过程;最后,能处理的数据对象十分广泛:适用于大规模的,高度非线性的,不完备的数据处理。本文以几种典型神经网络为例(BP神经网络、RBF神经网络、正交多项式基函数神经网络、样条基函数神经网络),对基于神经网络的函数逼近方法进行了研究。神经网络的函数逼近能力受神经元个数、学习率、学习次数和训练目标等因素的影响,因此,在研究过程中,充分运用神经网络的非线性逼近能力,首先对几种用于函数逼近的神经网络的结构及算法进行研究;再针对几种常用函数曲线,如正弦函数、指数函数、对数函数、三角函数等,分别用典型神经网络进行逼近,并对逼近效果进行比较,得到用于函数逼近的神经网络选取规律。所得结论经过实际仿真测试,证明了其有效性。本文的研究结果对函数逼近的研究具有借鉴意义。更多还原

【Abstract】 Function approximation is one of the most important parts of the theory of functions which plays a very important role in the numerical computation. Using neural network to implement function approximation provides a new way to the development of function approximation.There are many advantages of using neural network to implement function approximation: First, it provides a standard approximation structure and approximation tool that can achieve arbitrary accuracy by changing the numbers of hidden layer; Second, there is a standard learning algorithm to determine the parameters of the approximation of functions, and the process is anthropopathic, namely a good simulation of the human learning process; Finally, it can deal with a wide range of data objects, such as a very large scale, highly non-linear, and incomplete data set.This paper takes several types of neural networks as the example(the BP neural network, the RBF neural network, the Orthogonal neural network and the Spline neural network).To study the methods of function approximation based on neural networks. The ability of function approximation is influenced by the numbers of neurons, learning rate, training objectives and so on. Therefore, to make a full use of the nonlinear approximation ability of neural networks in the process of the study, we should, first, make a study of structures and algorithms of the several neural networks, and then aiming at several kinds of conventional function curves, such as sine function, exponential function, logarithmic function, triangle waves and so on, compare experiment results of function approximation with typical neural network respectively to get the selection law of Neural Networks. All the conclusions are proved effective after the actual simulation test.The method studied by the article has significant reference for the research of function approximation.更多还原