On the convergence and application of Stirling's method

Volume 30 / 2003

Ioannis K. Argyros Applicationes Mathematicae 30 (2003), 109-119 MSC: 65B05, 65G99, 65J15, 65N30, 65N35, 47H17, 49M15. DOI: 10.4064/am30-1-7

Abstract

We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematics
    Cameron University
    Lawton, OK 73505, U.S.A.
    e-mail

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