Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 475320, 12 pages
doi:10.1155/2009/475320
The average errors for the Grünwald interpolation in the Wiener space
Yingfang Du1
and Huajie Zhao2
1College of Chemistry and Life Science, Tianjin Normal University, Tianjin 300387, China
2Department of Mathematics, Tianjin Normal University, Tianjin 300387, China
Abstract
We determine the weakly asymptotically orders for the average errors of the Grünwald interpolation sequences based on the Tchebycheff nodes in the Wiener space. By these results we know that for the Lp-norm (2≤q≤4) approximation, the p-average (1≤p≤4) error of some Grünwald interpolation sequences is weakly equivalent to the p-average errors of the best polynomial approximation sequence.