Table of Contents
Advances in Numerical Analysis
Volume 2016, Article ID 6758283, 10 pages
http://dx.doi.org/10.1155/2016/6758283
Research Article

Lebesgue Constant Using Sinc Points

1German University in Cairo, New Cairo City 11835, Egypt
2Faculty of Science, Ain Shams University, Cairo 11566, Egypt
3University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Received 20 April 2016; Revised 20 July 2016; Accepted 18 August 2016

Academic Editor: William J. Layton

Copyright © 2016 Maha Youssef et al. 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

Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases. A comparison between the obtained upper bound of Lebesgue constant using Sinc points and other upper bounds for different set of points, like equidistant and Chebyshev points, is introduced.