The Non-linear Approximation Characteristic Of The General Sobolev Space With Worst Case Setting

In this paper,we study the non-linear approximation characteristic of the general Sobolev space with worst case setting.We give the asymptotic degrees of the non一linear Alexandroff an.(w,x)-widths,the non-linear manifoldδ(w,x)-widths and the non-linear βn(w,x)-widths of Spr(T)(1≤p≤∞)in the Sq(T)-metric and the relationship among them, namelyan(BSpr(T),Sq(T))≈β(BSpr(T),Sq(T))≈δ(BSpr(T),Sq(T))≈n-r+1/q-1/p,1≤p,q≤∞Wherere BSpr(T)is the unit ball of the Spr(T).