On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence

Janak Raj Sharma, Sunil Kumar and Lorentz Jäntschi
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Janak Raj Sharma: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal Sangrur 148106, India
Sunil Kumar: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal Sangrur 148106, India
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2020, vol. 8, issue 7, 1-15

Abstract: A number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering this factor as motivational, here we present a class of optimal fourth order methods for computing multiple roots without using derivatives in the iteration. The iterative formula consists of two steps in which the first step is a well-known Traub–Steffensen scheme whereas second step is a Traub–Steffensen-like scheme. The Methodology is based on two steps of which the first is Traub–Steffensen iteration and the second is Traub–Steffensen-like iteration. Effectiveness is validated on different problems that shows the robust convergent behavior of the proposed methods. It has been proven that the new derivative-free methods are good competitors to their existing counterparts that need derivative information.

Keywords: multiple root solvers; composite method; weight-function; derivative-free method; optimal convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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