Nonlinear approximations of functions having mixed smoothness - Nguyen, Cuong Manh (Journal of Computer Science and Cybernetics, 2019)
For multivariate Besov-type classes U^a_p,θ of functions having nonuniform mixed smoothness ar^d_+, we obtain the asumptotic order of entropy numbers ε_n(U^a_p,θ,L_q) and non-linear widths ρ_n(U^a_p,θ,L_q) defined via pseudo-dimension. We obtain also the asymptotic order of optimal methods of adaptive sampling recovery in L_q-norm of functions in U^a_p,θ by sets of a finite capacity which is measured by their cardinality or pseudo-dimension.