Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation. Issue 3 (August 2014)

• Record Type: Journal Article
• Authors: Xu, Guiqiao; Zhang, Zheng
• Is Part Of: Numerical mathematics. Volume 7:Issue 3(2014)
• Page Start: 317
• Page End: 333
• Publication Date: 2014-08
• Subjects: 41A15, -- 65D07, -- 41A28; Piecewise cubic Hermite interpolation, -- Lp-norm, -- simultaneous approximation, -- equidistant knot, -- infinite-dimensional Kolmogorov width; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S1004897900000131
• Languages: English
• ISSNs: 1004-8979

Abstract

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.