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An Efficient Class of Traub–Steffensen-Type Methods for Computing Multiple Zeros

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India
Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 65;
Received: 5 May 2019 / Revised: 21 May 2019 / Accepted: 22 May 2019 / Published: 25 May 2019
(This article belongs to the Special Issue Special Functions and Their Applications)
Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that require only evaluations of three functions per iteration. Convergence of the proposed class is demonstrated by means of using a graphical tool, namely basins of attraction. Applicability of the methods is demonstrated through numerical experimentation on different functions that illustrates the efficient behavior. Comparison of numerical results shows that the presented iterative methods are good competitors to the existing techniques. View Full-Text
Keywords: nonlinear equations; multiple roots; derivative-free method; convergence nonlinear equations; multiple roots; derivative-free method; convergence
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Kumar, D.; Sharma, J.R.; Cesarano, C. An Efficient Class of Traub–Steffensen-Type Methods for Computing Multiple Zeros. Axioms 2019, 8, 65.

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