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Convergence behaviour of inexact Newton methods under weak Lipschitz condition. (English) Zbl 1092.65043
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 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.

65H10Systems of nonlinear equations (numerical methods)