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Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation

Published online by Cambridge University Press:  28 May 2015

Guiqiao Xu and
Zheng Zhang
Guiqiao Xu*
Affiliation:
Department of Mathematics, Tianjin Normal University, Tianjin, 300387, P.R. China
Zheng Zhang
Affiliation:
Department of Mathematics, Tianjin Normal University, Tianjin, 300387, P.R. China
*
*Corresponding author.Email address:Xuguiqiao@eyou.com
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Abstract

For the approximation in Lp-norm, we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots. For p = 1, ∞, we obtain its values. By these results we know that for the Sobolev classes, the approximation errors by piecewise cubic Hermite interpolation are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths. At the same time, the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.

Keywords

41A1565D0741A28Piecewise cubic Hermite interpolationLp-normsimultaneous approximationequidistant knotinfinite-dimensional Kolmogorov width

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 3 , August 2014, pp. 317 - 333
Copyright
Copyright © Global Science Press Limited 2014

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