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On the local convergence of a fifth-order iterative method in Banach spaces

Author

Listed:
  • Cordero, A.
  • Ezquerro, J.A.
  • Hernández-Verón, M.A.
  • Torregrosa, J.R.

Abstract

A new predictor–corrector iterative procedure, that combines Newton’s method as predictor scheme and a fifth-order iterative method as a corrector, is designed for solving nonlinear equations in Banach spaces. We analyze the local order of convergence and the regions of accessibility of the new method comparing it with Newton’s method, both theoretical and numerically.

Suggested Citation

  • Cordero, A. & Ezquerro, J.A. & Hernández-Verón, M.A. & Torregrosa, J.R., 2015. "On the local convergence of a fifth-order iterative method in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 396-403.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:396-403
    DOI: 10.1016/j.amc.2014.11.084
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    Cited by:

    1. Martínez, Eulalia & Singh, Sukhjit & Hueso, José L. & Gupta, Dharmendra K., 2016. "Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 252-265.
    2. Janak Raj Sharma & Harmandeep Singh & Ioannis K. Argyros, 2022. "A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    3. Lotfi, Taher & Assari, Paria, 2015. "New three- and four-parametric iterative with memory methods with efficiency index near 2," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 1004-1010.
    4. Sukhjit Singh & Eulalia Martínez & Abhimanyu Kumar & D. K. Gupta, 2020. "Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations," Mathematics, MDPI, vol. 8(3), pages 1-11, March.
    5. Singh, Sukhjit & Gupta, Dharmendra Kumar & Martínez, E. & Hueso, José L., 2016. "Semilocal and local convergence of a fifth order iteration with Fréchet derivative satisfying Hölder condition," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 266-277.

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