Geodesic
Improved ball convergence of Newton's method under general conditions
Ioannis K. Argyros 1   ; Hongmin Ren 2
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 College of Information and Electronics Hangzhou Polytechnic Hangzhou 311402, Zhejiang, P.R. China
Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 365-375 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.
DOI : 10.4064/am39-3-9
Keywords: present ball convergence results newtons method order approximate locally unique solution nonlinear operator equation banach space setting hypotheses involve general majorants chet derivatives operators involved special convex majorants results compared earlier have least large radius convergence tight error bounds distances involved precise information uniqueness solution

Ioannis K. Argyros  1   ; Hongmin Ren  2

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 College of Information and Electronics Hangzhou Polytechnic Hangzhou 311402, Zhejiang, P.R. China 
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Ioannis K. Argyros; Hongmin Ren. Improved ball convergence of Newton's
method under general conditions. Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 365-375. doi: 10.4064/am39-3-9

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