平面散乱数据一种渐近正定径向基函数插值与拟插值研究  

An Approximated Definite Radial Basis Interpolation and Quasi-interpolation for Scattered Data In Plane

作　　者：徐应祥[1] 薛鹏翔[2] 

机构地区：[1]中山大学新华学院,广东广州510520 [2]西安工业大学理学院,陕西西安710021

出　　处：《山西大学学报（自然科学版）》2017年第4期702-711,共10页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(10871160)

摘　　要：结合一元B样条和已有径向基函数的优点,提出了一种渐近正定径向基函数,并将其应用于平面散乱数据逼近,得到了一种新的插值格式和拟插值方法。数值例子表明,这种插值格式与拟插值方法对平面散乱数据均具有良好的逼近效果。Merging the advantages of B-spline and radial basis, a kind of approximated definite radial basis function was proposed and used for scattered data approximating in plane. A new interpolated form and a new quasi-interpolation were constructed. The numerical experiments show that the new interpolation and quasi-interpolation are all very efficient for approximating of scattered data in plane.

关 键 词：散乱数据 渐近正定 插值 拟插值 

分 类 号：O241.5[理学—计算数学] TP391.7[理学—数学]