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Zbl 1092.65043
Chen, Jinhai; Li, Weiguo
Convergence behaviour of inexact Newton methods under weak Lipschitz condition. (English)
[J] J. Comput. Appl. Math. 191, No. 1, 143-164 (2006). ISSN 0377-0427

The paper is concerned with solving iteratively systems of nonlinear equations by an inexact Newton method and by an inexact Newton-like method. The local convergence properties of these methods are discussed under weaker Lipschitz conditions than the affine invariant Lipschitz condition [see {\it B. Morini}, Math. Comput. 68, No. 228, 1605--1613 (1999; Zbl 0933.65050)], called center Lipschitz condition, respectively radius Lipschitz condition. The authors use, like other authors, an inexact Newton method and an inexact Newton-like method where a scaled relative residual control is performed at each iteration. The results obtained allow us to see how large the radius of the convergence ball is. Two concrete examples are given.
[Iulian Coroian (Baia Mare)]

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)

Keywords: system of nonlinear equations; inexact Newton method; inexact Newton-like methods; weak Lipschitz condition; affine invariant condition; numerical examples; local convergence; center Lipschitz condition; radius Lipschitz condition; residual control

Citations: Zbl 0933.65050

Cited in: Zbl 1216.65070 Zbl pre05853252 Zbl 1151.65044

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