Inexact Newton methods and recurrent functions

Volume 37 / 2010

Ioannis K. Argyros, Saïd Hilout Applicationes Mathematicae 37 (2010), 113-126 MSC: 65H10, 65J15, 65G99, 47H17, 49M15. DOI: 10.4064/am37-1-8

Abstract

We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner//outer iterations can be obtained. Furthermore, numerical examples are provided using polynomial, integral and differential equations.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematics Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    e-mail
  • Saïd HiloutLaboratoire de Mathématiques et Applications
    Poitiers University
    Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179
    86962 Futuroscope Chasseneuil Cedex, France
    e-mail

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