We investigate approximations of functions from the H\"older-Zygmund space of mixed smoothness H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d) defined on the d-dimensional unit cube \mathbb I ^d:=%DIFDELCMD < [%%% 0,1 ^d, by linear algorithms of sparse-grid sampling recovery and by deep ReLU (Rectified Linear Unit) neural networks when the dimension d may be very large.
<fluency> We investigate approximations of functions from the H\"older-Zygmund space of mixed smoothness H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d) defined on the d-dimensional unit cube \mathbb I ^d:=%DIFDELCMD < [%%% 0,1 ^d, by linear algorithms of sparse-grid sampling recovery and by deep ReLU (Rectified Linear Unit) neural networks when the dimension d may be very large.
We investigate approximations of functions from the H\"older-Zygmund space of mixed smoothness H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% defined on the d-dimensional unit cube \mathbb I ^d:=%DIFDELCMD < [%%% 0,1 ^d, by linear algorithms of sparse-grid sampling recovery and by deep ReLU (Rectified Linear Unit) neural networks when the dimension d may be very large.