Geodesic
On the convergence and application of Stirling's method
Ioannis K. Argyros1
1 Department of Mathematics Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 30 (2003) no. 1, pp. 109-119 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am30-1-7
Keywords: provide sufficient convergence conditions local semilocal convergence stirlings method locally unique solution nonlinear operator equation banach space setting contrast earlier results make basic restrictive assumption norm chet derivative operator involved strictly bounded above study concludes numerical example where results compare favorably earlier

Ioannis K. Argyros 1

1 Department of Mathematics Cameron University Lawton, OK 73505, U.S.A. 
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Ioannis K. Argyros. On the convergence and application
  of Stirling's method. Applicationes Mathematicae, Tome 30 (2003) no. 1, pp. 109-119. doi: 10.4064/am30-1-7

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