RBF网络及其在数值计算中的应用

Radius Basis Function Neural Networks and its Application in Numerical Calculation

由经典的函数逼近理论衍生的很多数值算法有共同的缺点:计算量大、适应性差,对模型和数据要求高,在实际应用中受到限制。神经网络可以被用来计算复杂输入与输出结果之间的关系,具有很强的函数逼近功能。文章阐述如何利用RBFNN进行函数逼近、求解非线性方程组以及散乱数据插值,结合MATLAB神经网络工具箱给出了数值实例,并与BP网络等方法进行了比较。应用结果表明RBFNN是数值计算的一个有力工具,与传统方法比较具有编程简单、实用的特点。

Many numeric algorithms derived from classical function approach theories have much flaw, such as too many complicated computation, bad adaptation, rigid demand for model and data and so on. So, they are restricted in the real application. Neural networks can be used to compute the relationship between complicated inputs and outputs, so neural networks have strong ability to approximate functions. How to solve functional approximating, nonlinear muhivariable equation systems and scattered data interpolation with RBFNN is elaborated in this paper. Simultaneously, numerical examples are given combining with the toolbox of MATLAB neural networks and experimental results are compared with some other methods. It is made clear that RBFNN is a powerful tool for numeric computation with easy computer programming. It has high value of application that RBFNN is made of software to resolve numerical problems.