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

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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.

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Acknowledgements

The corresponding author (Y.I. Kim) was supported by the Research Fund of Dankook University in 2012. In addition, the authors would like to give special thanks to anonymous referees for their valuable suggestions and comments as well as excellent english corrections on this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dankook University, Cheonan, 330-714, Korea

    Young Hee Geum & Young Ik Kim

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  1. Young Hee Geum
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  2. Young Ik Kim
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Correspondence to Young Ik Kim.

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Communicated by Ilio Galligani.

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Geum, Y.H., Kim, Y.I. An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations. J Optim Theory Appl 160, 608–622 (2014). https://doi.org/10.1007/s10957-013-0268-x

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  • DOI: https://doi.org/10.1007/s10957-013-0268-x

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