%0 Journal Article
%T The <i>m</i>-Point Quaternary Approximating Subdivision Schemes
%A Shahid S. Siddiqi
%A Muhammad Younis
%J American Journal of Computational Mathematics
%P 6-10
%@ 2161-1211
%D 2013
%I Scientific Research Publishing
%R 10.4236/ajcm.2013.31A002
%X <p align=\"justify\">
	<span style=\"font-family:Verdana;\">In this article, the objective is to introduce an algorithm to produce the quaternary </span><i><span style=\"font-family:Verdana;\">m</span></i><span style=\"font-family:Verdana;\">-point (for any integer </span><span style=\"font-family:Verdana;\">m&gt;1</span><span style=\"font-family:Verdana;\">) 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.</span><span></span> 
</p>
%K Cox-De Boor Recursion Formula
%K Quaternary
%K Approximating Subdivision Schemes
%K Convergence and Smoothness
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=30731