Journal of Applied Mathematics
Volume 2011 (2011), Article ID 832630, 13 pages
http://dx.doi.org/10.1155/2011/832630
Research Article

( 2 𝑛 − 1 ) -Point Ternary Approximating and Interpolating Subdivision Schemes

Muhammad Aslam,1 Ghulam Mustafa,2 and Abdul Ghaffar2

1Department of Mathematics, Lock Haven University, Lock Haven, PA 17745, USA
2The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Received 25 July 2011; Accepted 19 September 2011

Academic Editor: Hui-Shen Shen

Copyright © 2011 Muhammad Aslam 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

We present an explicit formula which unifies the mask of ( 2 𝑛 − 1 ) -point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that ( 2 𝑛 − 1 ) -point schemes are better than 2 𝑛 -scheme in the sense of computational cost, support and error bounds.