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Abstract and Applied Analysis
Volume 2009, Article ID 301967, 14 pages
http://dx.doi.org/10.1155/2009/301967
Research Article

A New 4-Point Quaternary Approximating Subdivision Scheme

Department of Mathematics, The Islamia University of Bahawalpur, 63100 Punjab, Pakistan

Received 2 September 2008; Revised 16 March 2009; Accepted 25 March 2009

Academic Editor: Boris Shekhtman

Copyright © 2009 Ghulam Mustafa and Faheem Khan. 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.

Citations to this Article [15 citations]

The following is the list of published articles that have cited the current article.

  • Ghulam Mustafa, and Muhammad Sadiq Hashmi, “Subdivision depth computation for n-ary subdivision curves/surfaces,” Visual Computer, vol. 26, no. 6-8, pp. 841–851, 2010. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, and Najma Abdul Rehman, “The mask of (2b+4)-point n-ary subdivision scheme,” Computing, vol. 90, no. 1-2, pp. 1–14, 2010. View at Publisher · View at Google Scholar
  • Costanza Conti, and Kai Hormann, “Polynomial reproduction for univariate subdivision schemes of any arity,” Journal of Approximation Theory, vol. 163, no. 4, pp. 413–437, 2011. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, Abdul Ghaffar, and Faheem Khan, “The Odd-Point Ternary Approximating Schemes,” American Journal of Computational Mathematics, vol. 01, no. 02, pp. 111–118, 2011. View at Publisher · View at Google Scholar
  • Abdul Ghaffar, and Ghulam Mustafa, “A Family of Even-Point Ternary Approximating Schemes,” ISRN Applied Mathematics, vol. 2012, pp. 1–14, 2012. View at Publisher · View at Google Scholar
  • Muhammad Aslam, and W. P. Abeysinghe, “Odd-Ary Approximating Subdivision Schemes and RS Strategy for Irregular Dense Initial Data,” ISRN Mathematical Analysis, vol. 2012, pp. 1–8, 2012. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, Jiansong Deng, Pakeeza Ashraf, and Najma Abdul Rehman, “The Mask of Odd Points -Ary Interpolating Subdivision Scheme,” Journal of Applied Mathematics, vol. 2012, pp. 1–20, 2012. View at Publisher · View at Google Scholar
  • S. Amat, and J. Liandrat, “On a nonlinear 4-point quaternary approximating subdivision scheme eliminating the Gibbs phenomenon,” SeMA Journal, 2013. View at Publisher · View at Google Scholar
  • Costanza Conti, and Lucia Romani, “Dual univariate -ary subdivision schemes of de Rham-type,” Journal of Mathematical Analysis and Applications, 2013. View at Publisher · View at Google Scholar
  • Hongchan Zheng, Shupei Huang, Feng Guo, and Guohua Peng, “Integer-point binary approximating subdivision schemes,” Journal of Information and Computational Science, vol. 11, no. 10, pp. 3387–3398, 2014. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, Pakeeza Ashraf, and Jiansong Deng, “Generalized and Unified Families of Interpolating Subdivision Schemes,” Numerical Mathematics-Theory Methods and Applications, vol. 7, no. 2, pp. 193–213, 2014. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, and Syeda Tehmina Ejaz, “Numerical Solution of Two-Point Boundary Value Problems by Interpolating Subdivision Schemes,” Abstract and Applied Analysis, vol. 2014, pp. 1–13, 2014. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, “Statistical and geometrical way of model selection for a family of subdivision schemes,” Chinese Annals of Mathematics, Series B, vol. 38, no. 5, pp. 1077–1092, 2017. View at Publisher · View at Google Scholar
  • Georg Muntingh, “Symbols and exact regularity of symmetric pseudo-splines of any arity,” BIT Numerical Mathematics, 2017. View at Publisher · View at Google Scholar
  • Ghulam Mustafa, Praveen Agarwal, and Robina Bashir, “A class of shape preserving 5-point n-ary approximating schemes,” Journal of Mathematics and Computer Science, vol. 18, no. 3, pp. 364–380, 2018. View at Publisher · View at Google Scholar