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A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions

Author

Listed:
  • Francisco I. Chicharro

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, Spain)

  • Rafael A. Contreras

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, Spain)

  • Neus Garrido

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, Spain)

Abstract

A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the constraints that the weight function must satisfy to achieve order three. In this sense, a family of iterative methods can be obtained with a suitable design of the weight function. That is, an iterative algorithm that depends on one or more parameters is designed. This family of iterative methods, starting with proper initial estimations, generates a sequence of approximations to the solution of a problem. A dynamical analysis is also included in the manuscript to study the long-term behavior of the family depending on the parameter value and the initial guess considered. This analysis reveals the good properties of the family for a wide range of values of the parameter. In addition, a numerical test on academic and engineering multiple-root functions is performed.

Suggested Citation

  • Francisco I. Chicharro & Rafael A. Contreras & Neus Garrido, 2020. "A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2194-:d:459443
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    References listed on IDEAS

    as
    1. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2017. "A family of optimal quartic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 1-21.
    2. Amiri, Abdolreza & Cordero, Alicia & Taghi Darvishi, M. & Torregrosa, Juan R., 2018. "Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 43-57.
    3. Behl, Ramandeep & Cordero, Alicia & Motsa, S.S. & Torregrosa, Juan R., 2015. "On developing fourth-order optimal families of methods for multiple roots and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 520-532.
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