Expanding the applicability of inexact Newton methods using restricted convergence domains

Volume 44 / 2017

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 44 (2017), 123-133 MSC: 65G99, 65H10, 47H17, 49M15. DOI: 10.4064/am2292-3-2016 Published online: 7 April 2017


We provide a new semilocal convergence analysis for the inexact Newton method in order to approximate a solution of a nonlinear equation in a Banach space setting. Using a new idea of restricted convergence domains we present a convergence analysis with the following advantages over earlier studies: larger convergence domain, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. This way we expand the applicability of the inexact Newton method. Special cases and numerical examples are also provided.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Santhosh GeorgeDepartment of Mathematical
    and Computational Sciences
    NIT Karnataka, India 575 025

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