多元散乱数据的渐近正定径向基函数插值  

APPROXIMATED DEFINITE RADIAL BASIS INTERPOLATION FOR MULTI-VARIABLES SCATTERED DATA

作　　者：张景岳 徐应祥[2] 薛鹏翔[3] Zhang Jingyue;Xu Yingxiang;Xue Pengxiang(Beijing Shusheng Electronic Technology Co,Ltd,Beijing 100029,China;Xinhua College,Sun Yatsen University,Guangzhou 510520,China;College of Science of Xi'an Technological University,Xi'an 71OO21China)

机构地区：[1]北京书生电子技术有限公司,北京341000 [2]中山大学新华学院,广州510520 [3]西安工业大学理学院,西安710021

出　　处：《数值计算与计算机应用》2018年第4期253-264,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(10871160)

摘　　要：本文以一元B样条和径向基函数为基础,构造了一种n元渐近正定径向基函数.因这种渐近正定径向基函数兼有一元B样条和已有径向基函数的优点,将其应用于n维欧氏空间的多元散乱数据插值,得到了一种新的高维散乱数据插值函数.数值例子表明,这种插值格式对n维欧氏空间多元散乱数据具有良好的逼近效果.In the paper,a kind of approximated definite radial basis function with n-variables has been constructed on the bases on one variable B-spline and radial basis function.Since the new approximated definite radial basis function have the advantages of B-spline and radial basis function,it can be used for scattered data interpolation in n dimension Euclidean space and a new higher dimension interpolated function has been obtained.Numerical experiments show that the new interpolation are very efficient for approximating of scattered data in n dimension Euclidean space.

关 键 词：散乱数据 渐近正定 插值 径向基. 

分 类 号：A15[哲学宗教—马克思主义哲学] D07[政治法律—政治学]