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A symmetric $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C^{3}$ non-stationary subdivision scheme

Published online by Cambridge University Press:  01 June 2014

S. S. Siddiqi
Affiliation:
Department of Mathematics, University of the Punjab, Lahore, Pakistan email shahidsiddiqiprof@yahoo.co.uk
M. Younis
Affiliation:
Department of Mathematics, University of the Punjab, Lahore, Pakistan email shahidsiddiqiprof@yahoo.co.uk

Abstract

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This paper proposes a new family of symmetric $4$-point ternary non-stationary subdivision schemes  that can generate the limit curves of $C^3$ continuity. The continuity of this scheme is higher than the existing 4-point ternary approximating schemes. The proposed scheme has been developed using trigonometric B-spline basis functions and analyzed using the theory of asymptotic equivalence. It has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some graphical and numerical examples are being considered, by choosing an appropriate tension parameter $0<\alpha <\pi /3 $, to show the usefulness of the proposed scheme. Moreover, the Hölder regularity and the reproduction property are also being calculated.

Type
Research Article
Copyright
© The Author(s) 2014 

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