On highly efficient simultaneous schemes for finding all polynomial roots

Mudassir Shams; Naila Rafiq; Nasreen Kausar; Praveen Agarwal; Nazir Ahmad Mir; Yong Min Li

doi:10.1142/S0218348X22401983

On highly efficient simultaneous schemes for finding all polynomial roots

Mudassir Shams
, Naila Rafiq
, Nasreen Kausar
, Praveen Agarwal
, Nazir Ahmad Mir
, Yong Min Li

Nonlinear Dynamic Research Centre (NDRC)

Riphah International University
National University of Modern Languages
Yildiz Technical University
International College of Engineering
People's Friendship University of Russia
International Center for Basic and Applied Sciences
Huzhou University
Hangzhou Normal University

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

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.

Original language	English
Article number	2240198
Journal	Fractals
Volume	30
Issue number	10
DOIs	https://doi.org/10.1142/S0218348X22401983
State	Published - 1 Dec 2022

Keywords

CPU-Time
Computational Efficiency
Convergence Order
Iterative Technique
Multiple Roots

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10.1142/S0218348X22401983

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abstract = "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.",

keywords = "CPU-Time, Computational Efficiency, Convergence Order, Iterative Technique, Multiple Roots",

author = "Mudassir Shams and Naila Rafiq and Nasreen Kausar and Praveen Agarwal and Mir, \{Nazir Ahmad\} and Li, \{Yong Min\}",

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AU - Shams, Mudassir

AU - Rafiq, Naila

AU - Kausar, Nasreen

AU - Agarwal, Praveen

AU - Mir, Nazir Ahmad

AU - Li, Yong Min

PY - 2022/12/1

Y1 - 2022/12/1

N2 - 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.

AB - 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.

KW - CPU-Time

KW - Computational Efficiency

KW - Convergence Order

KW - Iterative Technique

KW - Multiple Roots

UR - https://www.scopus.com/pages/publications/85143618404

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DO - 10.1142/S0218348X22401983

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JO - Fractals

JF - Fractals

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On highly efficient simultaneous schemes for finding all polynomial roots

Abstract

Keywords

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