International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 279-286

On approximation of functions and their derivatives by quasi-Hermite interpolation

G. Min

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.


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 (1x2)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.