# Generalization of Binary Tensor Product Schemes Depends upon Four Parameters

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 produce...

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Main Authors: , , Article English 2018-01-01 Mehran University Research Journal of Engineering and Technology http://publications.muet.edu.pk/index.php/muetrj/article/view/107
id doaj-fbe0ea0b4d494f56b5954f36e7a84f39 Article doaj-fbe0ea0b4d494f56b5954f36e7a84f392020-11-24T22:38:48ZengMehran University of Engineering and TechnologyMehran University Research Journal of Engineering and Technology0254-78212413-72192018-01-01371107Generalization of Binary Tensor Product Schemes Depends upon Four ParametersRobina Bashir0Mehwish Bari1Ghulam Mustafa2Department of Mathematics, The Islamia University, BahawalpurDepartment of Mathematics, The Islamia University, BahawalpurDepartment of Mathematics, The Islamia University, BahawalpurThis 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.http://publications.muet.edu.pk/index.php/muetrj/article/view/107 DOAJ English Article DOAJ Robina Bashir Mehwish Bari Ghulam Mustafa Robina Bashir Mehwish Bari Ghulam Mustafa Generalization of Binary Tensor Product Schemes Depends upon Four Parameters Mehran University Research Journal of Engineering and Technology Robina Bashir Mehwish Bari Ghulam Mustafa Robina Bashir Generalization of Binary Tensor Product Schemes Depends upon Four Parameters Generalization of Binary Tensor Product Schemes Depends upon Four Parameters Generalization of Binary Tensor Product Schemes Depends upon Four Parameters Generalization of Binary Tensor Product Schemes Depends upon Four Parameters Generalization of Binary Tensor Product Schemes Depends upon Four Parameters generalization of binary tensor product schemes depends upon four parameters Mehran University of Engineering and Technology Mehran University Research Journal of Engineering and Technology 0254-7821 2413-7219 2018-01-01 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. http://publications.muet.edu.pk/index.php/muetrj/article/view/107 AT robinabashir generalizationofbinarytensorproductschemesdependsuponfourparameters AT mehwishbari generalizationofbinarytensorproductschemesdependsuponfourparameters AT ghulammustafa generalizationofbinarytensorproductschemesdependsuponfourparameters 1725711903881166848