Convergence behaviour of inexact Newton methods under weak Lipschitz condition |
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| Affiliation: | 1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;2. School of Mathematics and Computational Sciences, University of Petroleum, Dongying 257061, Shandong Province, People''s Republic of China |
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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. |
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