Approximation Characteristic Of Function With Common Mixed Smoothness

In this paper,we investigate the approximation error of hypothesis space defined via Reproducing Kernel Hilbert Space,it can decays as Oln R-q（）for Inverse multiquadrics kernel and Gaussian kernel in function with common mixed smoothness,which use the approximation results of entire function and nodal function.that is:（1）For Inverse multiquadrics kernel （?）（2）For Gaussian kernel（?）Where f∈W^A₂（IR^d）,r satisfies the definition of 1.1.It generalizes Zhou’s study about the approximation error for Inverse multiquadrics kernel and Gaussian kernel in Sobolev space.