Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation

Advances in Difference Equations

Shaher Momani¹  Mudassir Shams²  Praveen Agarwal³  Nasreen Kausar⁴  Naila Rafiq⁵  Choonkil Park⁶ 

[1] College of Humanities and Sciences, Ajman University;Department of Mathematics and Statistics, Riphah International University I-14;Department of Mathematics, Anand International College of Engineering;Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University;Department of Mathematics, NUML;Department of Mathematics, Research Institute of Natural Science, Hanyang University;

关键词: Multiple roots;    Polynomial equation;    Iterative methods;    Simultaneous methods;    Computational efficiency and CPU-time;   

DOI  :  10.1186/s13662-021-03649-6

来源: DOAJ

【 摘 要 】

Abstract Two new iterative methods for the simultaneous determination of all multiple as well as distinct roots of nonlinear polynomial equation are established, using two suitable corrections to achieve a very high computational efficiency as compared to the existing methods in the literature. Convergence analysis shows that the orders of convergence of the newly constructed simultaneous methods are 10 and 12. At the end, numerical test examples are given to check the efficiency and numerical performance of these simultaneous methods.

【 授权许可】

Unknown