Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 317–333
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.1232nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 317–333
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Piecewise cubic Hermite interpolation $L_p$-norm simultaneous approximation equidistant knot infinite-dimensional Kolmogorov width.