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M. F. Hassan and N. A. Dodgson, “Ternary and Three Point Univariate Subdivision Schemes,” In: A. Cohen, J.-L. Merrien and L. L. Schumaker, Eds., Curve and Surface Fitting: Sant-Malo, Nashboro Press, Brentwood, 2003, pp. 199-208.

has been cited by the following article:

• TITLE: The m-Point Quaternary Approximating Subdivision Schemes

  AUTHORS: Shahid S. Siddiqi, Muhammad Younis

  KEYWORDS: Cox-De Boor Recursion Formula; Quaternary; Approximating Subdivision Schemes; Convergence and Smoothness

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.1A, April 30, 2013

  ABSTRACT: In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.