An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations

Young Hee Geum and Young Ik Kim ()
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Young Hee Geum: Dankook University
Young Ik Kim: Dankook University

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 2, No 13, 608-622

Abstract: Abstract This paper investigates an optimal family of derivative-free fast 16th-order multipoint iterative methods for solving nonlinear equations using polynomial weighting functions and a real control parameter. Convergence analyses and computational properties are shown along with a comparison of the classical work done by Kung–Traub in 1974. The underlying theoretical treatment and computational advantage of faster computing time is well supported through a variety of concrete numerical examples.

Keywords: 16th-Order convergence; Optimal order; Asymptotic error constant; Efficiency index; Derivative-Free (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0268-x

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