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Nonlinear approximations of functions having mixed smoothness

Cuong Manh Nguyen


For multivariate Besov-type classes $U^a_{p,\theta}$ of functions having nonuniform mixed smoothness  $a\in\rr^d_+$, we obtain the asumptotic order of entropy numbers $\epsilon_n(U^a_{p,\theta},L_q)$ and non-linear widths $\rho_n(U^a_{p,\theta},L_q)$ defined via pseudo-dimension.  We obtain also the asymptotic order of optimal methods of adaptive sampling recovery in $L_q$-norm of functions in $U^a_{p,\theta}$ by sets of a finite capacity which is measured by their cardinality or pseudo-dimension.


Besov-type spaces; Linear sampling recovery; Nonlinear adaptive sampling recovery

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Journal of Computer Science and Cybernetics ISSN: 1813-9663

Published by Vietnam Academy of Science and Technology