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Generalized and Unified Families of Interpolating Subdivision Schemes

Published online by Cambridge University Press:  28 May 2015

Ghulam Mustafa ,
Pakeeza Ashraf  and
Jiansong Deng
Ghulam Mustafa*
Affiliation:
Department of Mathematics, The Islamia University of Bahawalpur, Pakistan
Pakeeza Ashraf*
Affiliation:
University of Science and Technology of China, P.R. China
Jiansong Deng*
Affiliation:
University of Science and Technology of China, P.R. China
*
Corresponding author.Email address:ghulam.mustafa@iub.edu.pk, mustafa_rakib@yahoo.com
Corresponding author.Email address:pakeeza_ashraf@yahoo.com
Corresponding author.Email address:dengjs@ustc.edu.cn
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Abstract

We present generalized and unified families of (2n)-point and (2n — 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomial for any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-point interpolating schemes of lower and higher arity belong to this family of schemes. We also present tensor product version of generalized and unified families of schemes. Moreover error bounds between limit curves and control polygons of schemes are also calculated. It has been observed that error bounds decrease when complexity of the scheme decrease and vice versa. Furthermore, error bounds decrease with the increase of arity of the schemes. We also observe that in general the continuity of interpolating scheme do not increase by increasing complexity and arity of the scheme.

Keywords

65D1765D0765D05Interpolating subdivision schemeeven-ary schemesodd-ary schemesLagrange polynomialparameterserror boundstensor product
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 2 , May 2014 , pp. 193 - 213
Copyright
Copyright © Global Science Press Limited 2014

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