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 $a\in\rr^d_+$, 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.