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Local convergence of iterative methods for solving equations and system of equations using weight function techniques

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  • Argyros, Ioannis K.
  • Behl, Ramandeep
  • Tenreiro Machado, J.A.
  • Alshomrani, Ali Saleh

Abstract

This paper analyzes the local convergence of several iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space. It is shown that the local convergence of these methods depends of hypotheses requiring the first-order derivative and the Lipschitz condition. The new approach expands the applicability of previous methods and formulates their theoretical radius of convergence. Several numerical examples originated from real world problems illustrate the applicability of the technique in a wide range of nonlinear cases where previous methods can not be used.

Suggested Citation

  • Argyros, Ioannis K. & Behl, Ramandeep & Tenreiro Machado, J.A. & Alshomrani, Ali Saleh, 2019. "Local convergence of iterative methods for solving equations and system of equations using weight function techniques," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 891-902.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:891-902
    DOI: 10.1016/j.amc.2018.09.060
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    References listed on IDEAS

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    1. Artidiello, Santiago & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, Maria P., 2015. "Multidimensional generalization of iterative methods for solving nonlinear problems by means of weight-function procedure," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1064-1071.
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