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Open AccessArticle

On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives

1
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
2
Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
3
Institute of Doctoral Studies, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1452; https://doi.org/10.3390/sym11121452
Received: 23 October 2019 / Revised: 19 November 2019 / Accepted: 20 November 2019 / Published: 26 November 2019
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
Many optimal order multiple root techniques involving derivatives have been proposed in literature. On the contrary, optimal order multiple root techniques without derivatives are almost nonexistent. With this as a motivational factor, here we develop a family of optimal fourth-order derivative-free iterative schemes for computing multiple roots. The procedure is based on two steps of which the first is Traub–Steffensen iteration and second is Traub–Steffensen-like iteration. Theoretical results proved for particular cases of the family are symmetric to each other. This feature leads us to prove the general result that shows the fourth-order convergence. Efficacy is demonstrated on different test problems that verifies the efficient convergent nature of the new methods. Moreover, the comparison of performance has proven the presented derivative-free techniques as good competitors to the existing optimal fourth-order methods that use derivatives. View Full-Text
Keywords: iterative function; multiple root; composite method; derivative-free method; optimal convergence iterative function; multiple root; composite method; derivative-free method; optimal convergence
MDPI and ACS Style

Sharma, J.R.; Kumar, S.; Jäntschi, L. On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives. Symmetry 2019, 11, 1452.

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