2𝑛−1-Point Ternary Approximating and Interpolating Subdivision SchemesReport as inadecuate

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Journal of Applied MathematicsVolume 2011 2011, Article ID 832630, 13 pages

Research Article

Department of Mathematics, Lock Haven University, Lock Haven, PA 17745, USA

The 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.


We present an explicit formula which unifies the mask of 2𝑛−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 2𝑛−1-point schemes are better than 2𝑛-scheme in the sense of computational cost, support and error bounds.

Author: Muhammad Aslam, Ghulam Mustafa, and Abdul Ghaffar

Source: https://www.hindawi.com/


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