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Dimension-dependence error estimates for sampling recovery on Smolyak grids

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ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation

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 $u$ active variables ($1 le u le d$), 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 $d$, $u$, $m$ when $d$ and $m$ may be large. This is a joint work with Mai Xuan Thao, Hong Duc University, Thanh Hoa, Vietnam.

This talk is part of the Isaac Newton Institute Seminar Series series.

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