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On a class of optimal fourth order multiple root solvers without using derivatives

Publication Type : Journal Article

Publisher : Symmetry

Source : Symmetry (2019), 11, 1452; doi: 10.3390/sym11121452.

Url : https://www.mdpi.com/2073-8994/11/12/1452

Campus : Chennai

School : School of Engineering

Department : Mathematics

Year : 2019

Abstract : 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

Cite this Research Publication : Janak Raj Sharma, Sunil Kumar, Lorentz Jantschi “On a class of optimal fourth order multiple root solvers without using derivatives” Symmetry (2019), 11, 1452; doi: 10.3390/sym11121452.

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