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

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.