A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes

Aamir Shahzad, Faheem Khan, Abdul Ghaffar, Shao-Wen Yao, Mustafa Inc and Shafqat Ali
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Aamir Shahzad: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Faheem Khan: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Abdul Ghaffar: Department of Mathematics, Ghazi University D G Khan, D G Khan 32200, Pakistan
Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
Mustafa Inc: Department of Computer Engineering, Biruni University, Istanbul 34096, Turkey
Shafqat Ali: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Mathematics, 2021, vol. 9, issue 8, 1-20

Abstract: In this paper, an advanced computational technique has been presented to compute the error bounds and subdivision depth of quaternary subdivision schemes. First, the estimation is computed of the error bound between quaternary subdivision limit curves/surfaces and their polygons after k th-level subdivision by using l 0 order of convolution. Secondly, by using the error bounds, the subdivision depth of the quaternary schemes has been computed. Moreover, this technique needs fewer iterations (subdivision depth) to get the optimal error bounds of quaternary subdivision schemes as compared to the existing techniques.

Keywords: quaternary subdivision scheme; subdivision models; inequalities; convolution; error bound; subdivision depth; curves and surfaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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