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An analysis of a family of Maheshwari-based optimal eighth order methods

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  • Chun, Changbum
  • Neta, Beny

Abstract

In this paper we analyze an optimal eighth-order family of methods based on Maheshwari’s fourth order method. This family of methods uses a weight function. We analyze the family using the information on the extraneous fixed points. Two measures of closeness of an extraneous points set to the imaginary axis are considered and applied to the members of the family to find its best performer. The results are compared to a modified version of Wang–Liu method.

Suggested Citation

  • Chun, Changbum & Neta, Beny, 2015. "An analysis of a family of Maheshwari-based optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 294-307.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:294-307
    DOI: 10.1016/j.amc.2014.12.064
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    1. Neta, Beny & Chun, Changbum, 2014. "Basins of attraction for several optimal fourth order methods for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 103(C), pages 39-59.
    2. Chun, Changbum & Neta, Beny, 2015. "Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 74-91.
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    Cited by:

    1. Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2017. "Generating function method for constructing new iterations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 414-423.
    2. Chun, Changbum & Neta, Beny, 2016. "Comparison of several families of optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 762-773.

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