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Monte Carlo methods for $L_q$ approximation on periodic Sobolev spaces with mixed smoothness

Presented by: 
Heping Wang Capital Normal University
Thursday 21st February 2019 - 11:40 to 12:15
INI Seminar Room 1
In this talk we consider multivariate approximation of compact embeddings of periodic Sobolev spaces of dominating mixed smoothness into the $L_q,\ 2< q\leq \infty$ space by linear Monte Carlo methods that use arbitrary linear information. We construct linear Monte Carlo methods and obtain explicit-in-dimension upper estimates. These estimates catch up with the rate of convergence.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons