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Improved local convergence analysis of inexact Newton-like methods under the majorant condition

Volume 42 / 2015

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 42 (2015), 343-357 MSC: 90C30, 65G99, 65K10, 47H17, 49M15. DOI: 10.4064/am2240-11-2015 Published online: 25 November 2015

Abstract

We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.

Authors

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

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