Generalization of Binary Tensor Product Schemes Depends upon Four Parameters

  • Robina Bashir Department of Mathematics, The Islamia University, Bahawalpur
  • Mehwish Bari Department of Mathematics, The Islamia University, Bahawalpur
  • Ghulam Mustafa Department of Mathematics, The Islamia University, Bahawalpur

Abstract

This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes.

Published
Jan 1, 2018
How to Cite
BASHIR, Robina; BARI, Mehwish; MUSTAFA, Ghulam. Generalization of Binary Tensor Product Schemes Depends upon Four Parameters. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 37, n. 1, p. 8, jan. 2018. ISSN 2413-7219. Available at: <http://publications.muet.edu.pk/index.php/muetrj/article/view/107>. Date accessed: 26 apr. 2018. doi: http://dx.doi.org/10.22581/muet1982.1801.10.
This is an open Acess Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License