Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Korea. Hamed H. Alsulami - Nonlinear Analysis and Applied Mathematics Research Group, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Arif Rafiq - Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan. Abdul Aziz Shahid - Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan.
The aim of this paper is to present a modification of the visualization process of finding the roots of a given complex polynomial. In this paper S-iteration scheme is used instead of standard Picard iteration. The word “polynomiography" coined by Kalantari for that visualization process. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. By using S-iteration scheme we obtain quite new nicely looking polynomiographs that are different from standard Picard iteration. Presented examples show that we obtain very interesting patterns for complex polynomial equations, permutation and doubly stochastic matrices. We believe that the results of this paper enrich the functionality of the existing polynomiography software.
Shin Min Kang, Hamed H. Alsulami, Arif Rafiq, Abdul Aziz Shahid, S-iteration scheme and polynomiography, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 617--627
Kang Shin Min, Alsulami Hamed H., Rafiq Arif, Shahid Abdul Aziz, S-iteration scheme and polynomiography. J. Nonlinear Sci. Appl. (2015); 8(5):617--627
Kang, Shin Min, Alsulami, Hamed H., Rafiq, Arif, Shahid, Abdul Aziz. "S-iteration scheme and polynomiography." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 617--627
