Linear Approximation Characteristic Of Sobolev Space With Bounded Mixed Derivative In Different Computational Setting

It’s important to find the most economical algorithm in lots of algorithms due to thelimited computational resources. That is what should be done in the computationalcomplexity. There is a close relationship between computational complexity and widthsin many Literatures[7,8,9]in recent decades. They always translate the problems of complexityin different computational case settings into computational the widths of the correspondingfunction classes. In this paper, we study the linear approximation characteristics in differentcomputational case settings of multivariate Sobolev spaceΜW r2(T d)with mixed derivativewhich using the method of discretization, and also calculate the asymptotic orders incorresponding computational case setting ofΜ Wr d2(T)in theS(Τ dq)(1≤q≤∞)-metric.