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The average errors for hermite interpolation on the 1-Fold integrated wiener space

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Abstract

For the weighted approximation in L p -norm, the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space. By this result, it is known that in the sense of information-based complexity, if permissible information functionals are Hermite data, then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Normal University, Tianjin, 300387, China

    Guiqiao Xu & Jingrui Ning

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  1. Guiqiao Xu
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  2. Jingrui Ning
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Correspondence to Guiqiao Xu.

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Xu, G., Ning, J. The average errors for hermite interpolation on the 1-Fold integrated wiener space. Chin. Ann. Math. Ser. B 33, 737–750 (2012). https://doi.org/10.1007/s11401-012-0731-2

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  • DOI: https://doi.org/10.1007/s11401-012-0731-2

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