Adaptive Monte Carlo Way In Information-based Complexity Of Functions With Common Mixed Smoothness

In this paper, the information-based complexity of Sobolev space W A(Tdp)withcommon mixed smoothness in the L(Tdq)-metric (1<p,q<∞) is investigated which usethe method of discretization of V. E. Maiorov and the properties of pseudo-scale, and theasymptotic order of the n-term adaptive Gel’fand MonteCarloapproximatione MCn(I,SWA(Td),L(Tdpq))is calculated. NamelyLet1<p,q<∞，and A is a finite subset ofR d，0∈intN(A(μ)). Thenwherer and v satisfy the definition of (1.3).