A MULTIVARIATE MULTIQUADRIC QUASI-INTERPOLATION WITH QUADRIC REPRODUCTION  

作　　者：Renzhong Feng Xun Zhou 

机构地区：[1]School of Mathematics and Systematic Science,Beijing University of Aeronautics and Astronautics,Beijing 100191,China [2]Key Laboratory of Mathematics,Informatics and Behavioral Semantics,Ministry of Education,China

出　　处：《Journal of Computational Mathematics》2012年第3期311-323,共13页计算数学（英文）

摘　　要：In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.

关 键 词：QUASI-INTERPOLATION Multiquadric functions Polynomial reproduction ：Pn-exact A-discretization of ：Da Approximation error. 

分 类 号：O174.42[理学—数学] O241.3[理学—基础数学]