The Research On The Method Of Selecting Shape Parameters In Radial Basis Function Interpolation

Radial basis function method is an effective tool to describe multivariate functions with one variable function in essence.It is widely used in approximation theory,numerical analysis,computational geometry and data processing.The shape parameters of radial basis function have great influence on the interpolation accuracy.Therefore,how to select shape parameters to minimize the interpolation error has been widely concerned by scholars at home and abroad.This paper focuses on the adaptive selection of shape parameters in radial basis function interpolation.The specific work includes the following three parts:Firstly,the basic theory of radial basis function is introduced.It includes the definition of radial basis function,several commonly used radial basis function and its application;the definition of radial basis function interpolation and the conditions for existence of unique solution of interpolation.The error estimation methods of radial basis function interpolation are summarized.Secondly,combined with the error theory of radial basis function interpolation,the selection methods of shape parameters in constant parameter radial basis function and variable parameter radial basis function are summarized respectively,and the comparison between the two methods is carried out through numerical experiments.In order to improve the interpolation accuracy of variable parameter radial basis function,Lagrange method and radial basis function method are combined to make better.Finally,the selection algorithm of shape parameters in radial basis function interpolation is introduced,and the optimal shape parameters of trigonometric function are obtained by Matlab interpolation numerical experiment using Gauss radial basis function.The relations between the shape parameters,the original function and interpolation error are analyzed and discussed.Based on Fourier series theory,the change of optimal shape parameters with Fourier coefficients is studied.By analyzing the data obtained from numerical experiments,the rules for selecting shape parameters of finite terms trigonometric series are summarized.The range of optimal shape parameters for a class of functions satisfying the Dirichlet convergence condition is obtained.The value of Fourier coefficient is randomly selected for numerical experiment,The feasibility and effectiveness of this conclusion are verified.It provides great convenience for the application of radial basis function method in practical engineering field,and has important scientific research value.Figure 31;Table 12;Reference 63...