Nonlinear approximations of functions having mixed smoothness
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DOI:
https://doi.org/10.15625/1813-9663/35/2/13578Keywords:
Besov-type spaces, Linear sampling recovery, Nonlinear adaptive sampling recoveryAbstract
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.Downloads
Published
03-06-2019
How to Cite
[1]C. M. Nguyen, “Nonlinear approximations of functions having mixed smoothness”, J. Comput. Sci. Cybern., vol. 35, no. 2, p. 119–134, Jun. 2019.
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Section
Computer Science
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