径向基函数插值逼近的误差分析

The Error Analysis of Radial Basis Function Interpolation and Approximation

函数逼近是数学规划中一个基本的问题,近年来,国内外的一些学者对径向基函数插值逼近问题进行了广泛的研究,对于某些测试函数来说,径向基插值相对于经典的插值方法,如牛顿插值、拉格朗日插值来说,在CPU时间、逼近程度等方面有着一定的优势,因此径向基函数插值成为解决散乱数据插值的一种新的有效的方法.将采用几种常见的径向基函数来逼近一元函数、二元函数,进行数值试验以及误差分析,并对径向基函数中的参数进行分析,获得了良好的误差分析结果.

The function approximation is a basic problem in mathematical programming. In the past few years,some domestic and foreign scholars have extensively studied the radial basis function.For some test function,radial basis interpolation,compared with the classical interpolation methods such as Newton interpolation and Lagrange interpolation,has some advantages in terms of CPU time,and degree of approximation,so the radial basis function interpolation is a new effective method to solve the scattered data interpolation.This paper uses several common radial basis functions to approximate a univariate function and dual function for numerical experiment and error analysis and good error analysis results are obtained.