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C. Conti and K. Hormann, “Polynomial Reproduction for Univariate Subdivision Schemes of any Arity,” Journal of Approximation Theory, Vol. 163, No. 4, 2011, pp. 413-437. doi:10.1016/j.jat.2010.11.002

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.