Geodesic
An improved convergence analysis of Newton's method for twice Fréchet differentiable operators
Ioannis K. Argyros1 ; Sanjay K. Khattri2
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505-6377, U.S.A.
2 Department of Engineering Stord/Haugesund University College N-414 Stord, Norway
Applicationes Mathematicae, Tome 40 (2013) no. 4, pp. 459-481.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.
DOI : 10.4064/am40-4-6
Keywords: develop local semilocal convergence results newtons method order solve nonlinear equations banach space setting results compare favorably earlier utilizing lipschitz conditions second chet derivative operators involved numerical examples where convergence conditions satisfied earlier convergence conditions satisfied reported

Ioannis K. Argyros 1 ; Sanjay K. Khattri 2

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505-6377, U.S.A.
2 Department of Engineering Stord/Haugesund University College N-414 Stord, Norway 
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Ioannis K. Argyros; Sanjay K. Khattri. An improved convergence analysis of Newton's method for twice Fréchet differentiable operators. Applicationes Mathematicae, Tome 40 (2013) no. 4, pp. 459-481. doi : 10.4064/am40-4-6. http://geodesic.mathdoc.fr/articles/10.4064/am40-4-6/

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