Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 317–333
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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 Lp-norm simultaneous approximation equidistant knot infinite-dimensional Kolmogorov width.
-
The best constants in the Wirtinger inequality
Liu, Yongping | Wu, Wenyan | Xu, GuiqiaoInternational Journal of Wavelets, Multiresolution and Information Processing, Vol. 14 (2016), Iss. 06 P.1650048
https://doi.org/10.1142/S021969131650048X [Citations: 2] -
A kind of sharp Wirtinger inequality
Xu, Guiqiao | Liu, Zehong | Lu, WantingJournal of Inequalities and Applications, Vol. 2019 (2019), Iss. 1
https://doi.org/10.1186/s13660-019-2121-8 [Citations: 3] -
Exact Constants for Simultaneous Approximation of Sobolev Classes by Piecewise Hermite Interpolation
Xu, G. Q. | Liu, Y. P. | Xiong, L. Y.Analysis Mathematica, Vol. 45 (2019), Iss. 3 P.621
https://doi.org/10.1007/s10476-019-0985-y [Citations: 3]