Convergence behaviour of inexact Newton methods under weak Lipschitz condition

Authors:
Jinhai Chen;Weiguo Li
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong and School of Mathematics and Computational Sciences, University of Petroleum, Dongying, Shand ...;School of Mathematics and Computational Sciences, University of Petroleum, Dongying, Shandong Province, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

Under weak Lipschitz condition, local convergence properties of inexact Newton methods and Newton-like methods for systems of nonlinear equations are established in an arbitrary vector norm. Processes with modified relative residual control are considered; the results easily provide an estimate of convergence ball for inexact methods. For a special case, the results are affine invariant. Some applications are given.