On highly efficient simultaneous schemes for finding all polynomial roots

This paper develops optimal family of fourth-order iterative techniques in order to find a single root and to generalize them for simultaneous finding of all roots of polynomial equation. Convergence study reveals that for single root finding methods, its optimal convergence order is 4, while for simultaneous methods, it is 12. Computational cost and numerical illustrations demonstrate that the newly developed family of methods outperformed the previous methods available in the literature. © 2022 The Author(s).

Authors
Shams M. , Rafiq N. , Kausar N. , Agarwal P. , Mir N.A. , Li Y.-M.
Journal
Fractals
Publisher
World Scientific Publishing Co.
Number of issue
10
Language
English
Status
Published
Link
External link
DOI
10.1142/S0218348X22401983
Number
2240198
Volume
30
Year
2022
Organizations
  • 1 Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, 44000, Pakistan
  • 2 Department of Mathematics, National University of Modern Languages (NUML), Islamabad, Pakistan
  • 3 Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, Istanbul, 34210, Turkey
  • 4 Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, 303012, India
  • 5 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
  • 6 Russian Federation and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates
  • 7 International Center for Basic and Applied Sciences, India, Jaipur, 302029, India
  • 8 Department of Mathematics, Huzhou University, Huzhou, 313000, China
  • 9 Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou, 311121, China
Keywords
Computational Efficiency; Convergence Order; CPU-Time; Iterative Technique; Multiple Roots
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