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Local convergence of two competing third order methods in Banach space

Volume 41 / 2014

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 41 (2014), 341-350 MSC: 65D10, 65D99, 65G99, 47H17, 49M15. DOI: 10.4064/am41-4-5


We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Santhosh GeorgeDepartment of Mathematical
    and Computational Sciences
    National Institute of Technology
    Karnataka, India 757 025

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