Random points are good for universal discretization

Feng, Dagan; V., Temlyakov,

doi:10.1016/j.jmaa.2023.127570

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…Remark 5. Recently, the papers [5,19] also derived new bounds on the complexity of sampling recovery in L 2 using non-linear algorithms. It is shown in [19,Thm.…”

Section: David Kriegmentioning

confidence: 99%

Tractability of sampling recovery on unweighted function classes

Krieg

2024

Proc. Amer. Math. Soc. Ser. B

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It is well-known that the problem of sampling recovery in the L 2 L_2 -norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as Hölder classes suffers from the curse of dimensionality. We show that the problem is tractable for those classes if they are intersected with the Wiener algebra of functions with summable Fourier coefficients. In fact, this is a relatively simple implication of powerful results from the theory of compressed sensing. Tractability is achieved by the use of non-linear algorithms, while linear algorithms cannot do the job.

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“…Remark 5. Recently, the papers [5,19] also derived new bounds on the complexity of sampling recovery in L 2 using non-linear algorithms. It is shown in [19,Thm.…”

Section: David Kriegmentioning

confidence: 99%

Tractability of sampling recovery on unweighted function classes

Krieg

2024

Proc. Amer. Math. Soc. Ser. B

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show abstract

“…Remark 5. Recently, the papers [5,19] also derived new bounds on the complexity of sampling recovery in L 2 using non-linear algorithms. It is shown in [19,Thm.…”

Section: David Kriegmentioning

confidence: 99%

Untitled

2024

Proc. Amer. Math. Soc. Ser. B

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It is well-known that the problem of sampling recovery in the L 2norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as Hölder classes suffers from the curse of dimensionality. We show that the problem is tractable for those classes if they are intersected with the Wiener algebra of functions with summable Fourier coefficients. In fact, this is a relatively simple implication of powerful results from the theory of compressed sensing. Tractability is achieved by the use of non-linear algorithms, while linear algorithms cannot do the job.We consider the problem of recovering a high-dimensional function f : [0, 1] d → C from a class F d using algorithms of the form (1)A n :with sampling points x j ∈ [0, 1] d and a recovery map φ : C n → L 2 . The error is measured in the L 2 -norm and in a worst-case setting, i.e., err(A n , F d , L 2 ) := sup

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Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness

Dũng

2024

Acta Math Vietnam

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Random points are good for universal discretization

Cited by 8 publications

References 14 publications

Tractability of sampling recovery on unweighted function classes

Tractability of sampling recovery on unweighted function classes

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Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness

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