TY - JOUR
T1 - Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation
AU - Guiqiao Xu & Zheng Zhang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 317
EP - 333
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1232nm
UR - https://global-sci.org/intro/article_detail/nmtma/5877.html
KW - Piecewise cubic Hermite interpolation, $L_p$-norm, simultaneous approximation,
equidistant knot, infinite-dimensional Kolmogorov width.
AB - <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>