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.