利用Gaussian核对多元函数的近似逼近及其误差估计  

Error Estimates for Approximate Approximations with Gaussian Kernels on Multivariate Compact Intervals

作　　者：徐艳艳[1] 陈广贵[1] 雷文慧[1] 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《四川师范大学学报（自然科学版）》2009年第5期581-587,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671019);教育部博士点基金(20050027007);四川省科技厅重点项目基金(05JY029-138)资助项目

摘　　要：V.Maz’ya首次提出了近似逼近法,其主要是研究定义在全空间上的光滑函数的逼近情况,但它不能有效的处理积分和拟微分算子的高阶求积公式问题及利用更有效的数值和半数值方法解决数学物理的边界等问题.F.M櫣ller和W.Varnhorn给出了一维紧区间上函数的近似逼近方法,而且还可以控制近似逼近的截断误差.根据上述思想,采用近似逼近法,利用Gaussian核对二维紧空间上光滑函数进行逼近,并考察由这种近似逼近法所产生的误差情况.Maz’ya introduced a method of approximate approximations which had mainly been used for functions defined on the whole space. However,it was difficult for this method to treat the differential equations and boundary integral equations. Then,F. Müller and W. Varnhorn applied the method of approximate approximation to functions which are defined on compact intervals and investigated the error. In this paper,we study approximate approximation with Gaussian kernels on multivariate compact intervals as well as the error estimates.

关 键 词：Gaussian核 近似逼近数 全误差 TAYLOR公式 

分 类 号：O174.41[理学—数学]