Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography
In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its <i>s</i>-convexity. We present some graphical examples showing the dynamics of the new iteration in the colouring and shapes of the obtained polynomio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3324 |
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| author | Lateef Olakunle Jolaoso Safeer Hussain Khan Kazeem Olalekan Aremu |
| author_facet | Lateef Olakunle Jolaoso Safeer Hussain Khan Kazeem Olalekan Aremu |
| author_sort | Lateef Olakunle Jolaoso |
| collection | DOAJ |
| description | In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its <i>s</i>-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 <i>s</i> in the <i>s</i>-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. |
| first_indexed | 2024-03-09T23:15:48Z |
| format | Article |
| id | doaj.art-9f8886ccf26d402584c19a109869d51e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:48Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9f8886ccf26d402584c19a109869d51e2023-11-23T17:36:39ZengMDPI AGMathematics2227-73902022-09-011018332410.3390/math10183324Dynamics of RK Iteration and Basic Family of Iterations for PolynomiographyLateef Olakunle Jolaoso0Safeer Hussain Khan1Kazeem Olalekan Aremu2Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South AfricaAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54000, PakistanDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South AfricaIn this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its <i>s</i>-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 <i>s</i> in the <i>s</i>-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.https://www.mdpi.com/2227-7390/10/18/3324polynomiographsRK iterationNewton methodbasic family of iterationsiterative processbasin of attractions |
| spellingShingle | Lateef Olakunle Jolaoso Safeer Hussain Khan Kazeem Olalekan Aremu Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography Mathematics polynomiographs RK iteration Newton method basic family of iterations iterative process basin of attractions |
| title | Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography |
| title_full | Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography |
| title_fullStr | Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography |
| title_full_unstemmed | Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography |
| title_short | Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography |
| title_sort | dynamics of rk iteration and basic family of iterations for polynomiography |
| topic | polynomiographs RK iteration Newton method basic family of iterations iterative process basin of attractions |
| url | https://www.mdpi.com/2227-7390/10/18/3324 |
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