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Dimension-dependence error estimates for sampling recovery on Smolyak grids

Presented by: 
Dũng Dinh Vietnam National University
Wednesday 20th February 2019 - 09:40 to 10:15
INI Seminar Room 1

We investigate dimension-dependence estimates of the approximation error for linear algorithms of sampling recovery on Smolyak grids parametrized by $m$, of periodic $d$-variate functions from the space with Lipschitz-H\"older mixed smoothness $\alpha > 0$. For the subsets of the unit ball in this space of functions with homogeneous condition and of functions depending on $\nu$ active variables ($1 \le \nu \le d$), respectively, we prove some upper bounds and lower bounds (for $\alpha \le 2$) of the error of the optimal sampling recovery on Smolyak grids, explicit in $d$, $\nu$, $m$ when $d$ and $m$ may be large. This is a joint work with Mai Xuan Thao, Hong Duc University, Thanh Hoa, Vietnam.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons