| Autor: |
Byrenheid, Glenn, Kunsch, Robert J., Nguyen, Van Kien |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.jco.2017.12.002 |
| Popis: |
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\mathbb{T}^d$ into the space $L_{\infty}(\mathbb{T}^d)$ via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to $1/2$ in the main rate compared to the worst case approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan. |
| Databáze: |
arXiv |
| Externí odkaz: |
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