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Multidimensional generalization of iterative methods for solving nonlinear problems by means of weight-function procedure

Author

Listed:
  • Artidiello, Santiago
  • Cordero, Alicia
  • Torregrosa, Juan R.
  • Vassileva, Maria P.

Abstract

In this paper, from Traub’s method and by applying weight function technique, a bi-parametric family of predictor–corrector iterative schemes with optimal fourth-order of convergence, for solving nonlinear equations, is presented. By using some algebraic manipulations and a divided difference operator, we extend this family to the multidimensional case, preserving its order of convergence. Some numerical test are made in order to confirm the theoretical results and to compare the new methods with other known ones.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:1064-1071
    DOI: 10.1016/j.amc.2015.07.024
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    Citations

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    Cited by:

    1. Ramandeep Behl & Ioannis K. Argyros, 2020. "A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    2. Raudys R. Capdevila & Alicia Cordero & Juan R. Torregrosa, 2019. "A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    3. José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    4. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2017. "Stable high-order iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 70-88.
    5. 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.
    6. Ramandeep Behl & Ioannis K. Argyros & Jose Antonio Tenreiro Machado, 2020. "Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    7. Alzahrani, Abdullah Khamis Hassan & Behl, Ramandeep & Alshomrani, Ali Saleh, 2018. "Some higher-order iteration functions for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 80-93.
    8. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.

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