Generator,multiquadric generator,quasi-interpolation and multiquadric quasi-interpolation  

作　　者：WU Zong-min MA Li-min 

机构地区：[1]Shanghai Key Laboratory for Contemporary Applied Mathematics. School of Mathematical Sciences, Fudan University, Shanghai 200433, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第4期390-400,共11页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the 973program-2006CB303102;SGST 09DZ 2272900;NSFC No.11026089

摘　　要：The aim of this survey paper is to propose a new concept ＂generator＂. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.The aim of this survey paper is to propose a new concept ＂generator＂. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.

关 键 词：GENERATOR function representation approximation numerical differentiation multiquadric quasi-interpolation 

分 类 号：O241.3[理学—计算数学] TM31[理学—数学]