Rational Quasi-Interpolation Approximation of Scattered Data in R^(3)  

作　　者：Renzhong Feng Lifang Song 

机构地区：[1]School of Mathematics and Systematic Science&Key Laboratory of Mathematics,Informatics and Behavioral Semantics,Ministry of Education,Beijing University of Aeronautics and Astronautics,Beijing 100191,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2018年第1期169-186,共18页高等学校计算数学学报（英文版）

基　　金：The work was supported by the National Natural Science Foundation of China(No.11271041,No.91630203);CASP of China Grant(No.MJ-F-2012-04).

摘　　要：This paper is concerned with a piecewise smooth rational quasi-interpolation with algebraic accuracy of degree(n+1)to approximate the scattered data in R 3.We firstly use the modified Taylor expansion to expand the mean value coordinates interpolation with algebraic accuracy of degree one to one with algebraic accuracy of degree(n+1).Then,based on the triangulation of the scattered nodes in R^(2),on each triangle a rational quasi-interpolation function is constructed.The constructed rational quasi-interpolation is a linear combination of three different expanded mean value coordinates interpolations and it has algebraic accuracy of degree(n+1).By comparing accuracy,stability,and efficiency with the C^(1)-Tri-interpolation method of Goodman[16]and the MQ Shepard method,it is observed that our method has some computational advantages.

关 键 词：Scattered data mean value coordinates interpolation modified Taylor expansion rational quasi-interpolation algebraic accuracy 

分 类 号：O17[理学—数学]