International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 279-286
doi:10.1155/S0161171296000385
On approximation of functions and their derivatives by quasi-Hermite interpolation
CECM, Department of Mathematics and Statistics, Simon Fraser University, B.C., Burnaby V5A 1S6, Canada
Received 2 April 1991; Revised 18 April 1994
Copyright © 1996 G. Min. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we consider the simultaneous approximation of the derivatives of the
functions by the corresponding derivatives of quasi-Hermite interpolation based on the zeros of (1−x2)pn(x) (where pn(x)is a Legendre polynomial). The corresponding approximation degrees are given.
It is shown that this matrix of nodes is almost optimal.