@Article{NMTMA-7-317,
author = {Guiqiao Xu and Zheng Zhang},
title = {Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2014},
volume = {7},
number = {3},
pages = {317--333},
abstract = {<p style="text-align: justify;">For the approximation in $L_p$-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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.1232nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5877.html}
}