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

Guiqiao Xu; Jingrui Ning

doi:10.1007/s11401-012-0731-2

Chinese Annals of Mathematics, Series B ›› 2012, Vol. 33 ›› Issue (5) : 737 -750. DOI: 10.1007/s11401-012-0731-2

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

Guiqiao Xu ¹^,^a
, Jingrui Ning ¹

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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.

Keywords

Chebyshev polynomial / Hermite interpolation / Weighted L _p-norm / 1-Fold integrated Wiener space

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Guiqiao Xu, Jingrui Ning. The average errors for hermite interpolation on the 1-Fold integrated wiener space. Chinese Annals of Mathematics, Series B, 2012, 33(5): 737-750 DOI:10.1007/s11401-012-0731-2

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