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On the approximation of mth power divided differences preserving the local order of convergence

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  • Amiri, Abdolreza
  • Argyros, Ioannis K.

Abstract

In this paper, some extensions are presented for a new technique to construct a family of divided differences that has been proposed previously. By applying a new definition for local order of convergence and presenting a comprehensive analysis, the relation between local order of convergence and R-order and Q-order is investigated. We also propose a new technique to approximate the elements of the developed divided differences. The divided differences are approximated by using the new scheme and are replaced in some iterative methods. Numerical experiments show that new derivative-free iterative methods obtained in this way are with high order of convergence. Numerical results confirm the theoretical results and indicate the efficiency and robustness of the new Jacobian-free methods.

Suggested Citation

  • Amiri, Abdolreza & Argyros, Ioannis K., 2021. "On the approximation of mth power divided differences preserving the local order of convergence," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s009630032100504x
    DOI: 10.1016/j.amc.2021.126415
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    References listed on IDEAS

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    1. Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    2. Miquel Grau-Sánchez & Miquel Noguera & José M. Gutiérrez, 2014. "Frozen Iterative Methods Using Divided Differences “à la Schmidt–Schwetlick”," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 931-948, March.
    3. 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.
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