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On the Power of Standard Information for Weighted Approximation

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Abstract.

We study weighted approximation of multivariate functions for classes of standard and linear information in the worst case and average case settings. Under natural assumptions, we show a relation between n th minimal errors for these two classes of information. This relation enables us to infer convergence and error bounds for standard information, as well as the equivalence of tractability and strong tractability for the two classes.

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Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, 40506, Lexington, KY, USA

    G. W. Wasilkowski

  2. Department of Computer Science, Columbia University, 10027, New York, NY, USA

    H. Wozniakowski

  3. Institute of Applied Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    H. Wozniakowski

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  1. G. W. Wasilkowski
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  2. H. Wozniakowski
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Wasilkowski, G., Wozniakowski, H. On the Power of Standard Information for Weighted Approximation. Found. Comput. Math. 1, 417–434 (2001). https://doi.org/10.1007/s102080010016

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  • DOI: https://doi.org/10.1007/s102080010016

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