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- W3017325642 abstract "It was recently shown by D. Krieg and M. Ullrich that, for L2-approximation of functions from a reproducing kernel Hilbert space, function values are almost as powerful as arbitrary linear information if the approximation numbers are square-summable. That is, en≲1kn∑j≥knaj2withkn≍nln(n),where en are the sampling numbers and ak are the approximation numbers. In particular, if (ak)∈ℓ2, then en and an are of the same polynomial order. For this, we presented an explicit (weighted least squares) algorithm based on i.i.d. random points and proved that this works with positive probability. This implies the existence of a good deterministic sampling algorithm. Here, we present a modification of our proof that shows that the same algorithm works with probability at least 1−n−c for any given c>0." @default.
- W3017325642 created "2020-04-24" @default.
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- W3017325642 date "2020-10-01" @default.
- W3017325642 modified "2023-10-01" @default.
- W3017325642 title "On the worst-case error of least squares algorithms for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e27 altimg=si11.svg><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-approximation with high probability" @default.
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- W3017325642 doi "https://doi.org/10.1016/j.jco.2020.101484" @default.
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