ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS-Reference-Cited by-同舟云学术

ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS

Published:2022-11-25 Issue:10 Volume:30 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

SHAMS MUDASSIR¹,RAFIQ NAILA²,KAUSAR NASREEN³,AGARWAL PRAVEEN⁴⁵⁶⁷,MIR NAZIR AHMAD²,LI YONG-MIN⁸⁹

Affiliation:

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 34210, Istanbul, Turkey

4. Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India

5. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia

6. Russian Federation and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

7. International Center for Basic and Applied Sciences, Jaipur 302029, India

8. Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China

9. Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

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.

Funder

NBHM

Ministry of Science and High Education of the Russian Federation and the Peoples Friendship University of Russia

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X22401983

Reference30 articles.

1. A modified Newton method for polynomials

2. A posteriori error bounds for the zeros of polynomials

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