Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography

Lateef Olakunle Jolaoso (), Safeer Hussain Khan and Kazeem Olalekan Aremu
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Lateef Olakunle Jolaoso: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South Africa
Safeer Hussain Khan: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54000, Pakistan
Kazeem Olalekan Aremu: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South Africa

Mathematics, 2022, vol. 10, issue 18, 1-16

Abstract: In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its s -convexity. We present some graphical examples showing the dynamics of the new iteration in the colouring and shapes of the obtained polynomiographs compared to the ones from the basic family only. Moreover, the computational results reveal that the value of s in the s -convex combination of the RK iteration has a significant impact on the time taken by the iteration process for approximating the roots of the polynomials. The obtained results are interesting from an artistic and computational point of view.

Keywords: polynomiographs; RK iteration; Newton method; basic family of iterations; iterative process; basin of attractions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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