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International Journal of Mathematics and Mathematical SciencesVolume 2013 2013, Article ID 893414, 8 pages

Research ArticleDepartment of Mathematics, The Islamia University of Bahawalpur, Punjab, Bahawalpur 63100, Pakistan

Received 27 July 2013; Revised 27 September 2013; Accepted 27 September 2013

Academic Editor: Palle E. Jorgensen

Copyright © 2013 Ghulam Mustafa and Robina Bashir. 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 efficient and simple algorithm to generate 4-point n-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-point n-ary interpolating schemes generated by completely different frameworks i.e., Lagrange interpolant and wavelet theory can also be generated by the proposed algorithm. Furthermore, we have discussed continuity, Hölder regularity, degree of polynomial generation, polynomial reproduction, and approximation order of the schemes.

Author: Ghulam Mustafa and Robina Bashir



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