Random sections of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e145" altimg="si11.svg"><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-ellipsoids, optimal recovery and Gelfand numbers of diagonal operators

Hinrichs, Aicke; Prochno, Joscha; Sonnleitner, Mathias

doi:10.1016/j.jat.2023.105919

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Gaussian Information1

Nonlinear Sampling Algorithms1

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2023

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Cited by 2 publications

(2 citation statements)

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“…In order to investigate the sharpness of the bound (4.7), in [59] random sections of p -ellipsoids have been studied which are images of p -balls with 0 < p ≤ ∞ under diagonal operators. In the case 1 < p ≤ ∞ the logarithmic gaps present for poly-log decay with α = 1/2 can be narrowed.…”

Section: Gaussian Informationmentioning

confidence: 99%

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On the power of iid information for linear approximation

Sonnleitner,

Ullrich

2023

J. App. Num. Analysis

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This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at random on a class of admissible information functionals. We present a general result based on a weighted least squares method and derive consequences for special cases. Improvements are available if the information is "Gaussian" or if we consider iid function values for Sobolev spaces. We include open questions to guide future research on the power of random information in the context of information-based complexity.

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Section: Gaussian Informationmentioning

confidence: 99%

“…We refer to [53] for more details on the proof of (5.2) which is based on 1 -minimization or basis pursuit and references to generalizations. Recently, this has been generalized to p -ellipsoids with implications for Gelfand numbers of diagonal operators, see [59].…”

Section: Nonlinear Sampling Algorithmsmentioning

confidence: 99%