Nonlinear approximations of functions having mixed smoothness

Cuong Manh Nguyen
Author affiliations

Authors

  • Cuong Manh Nguyen Nguyen Manh Cuong Department of Natural Sciences, Hong Duc University 565 Quang Trung,TP. Thanh Hoa, Vietnam E-mail: cuongnv.hdu@gmail.com

DOI:

https://doi.org/10.15625/1813-9663/35/2/13578

Keywords:

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

Abstract

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.

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Published

03-06-2019

How to Cite

[1]
C. M. Nguyen, “Nonlinear approximations of functions having mixed smoothness”, JCC, vol. 35, no. 2, p. 119–134, Jun. 2019.

Issue

Section

Computer Science