Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/26911
Title: Globally and superlinearly convergent inexact Newton-Krylov algorithms for solving nonsmooth equations
Authors: Chen, J
Qi, L 
Issue Date: 2010
Source: Numerical linear algebra with applications, 2010, v. 17, no. 1, p. 155-174
Abstract: This paper presents some variants of the inexact Newton method for solving systems of nonlinear equations defined by locally Lipschitzian functions. These methods use variants of Newton's iteration in association with Krylov subspace methods for solving the Jacobian linear systems. Global convergence of the proposed algorithms is established under a nonmonotonic backtracking strategy. The local convergence based on the assumptions of semismoothness and BD-regularity at the solution is characterized, and the way to choose an inexact forcing sequence that preserves the rapid convergence of the proposed methods is also indicated. Numerical examples are given to show the practical viability of these approaches.
Keywords: Global convergence
Inexact newton method
Krylov subspace methods
Nonmonotonic technique
Nonsmooth analysis
Superlinear convergence
Publisher: John Wiley & Sons
Journal: Numerical linear algebra with applications 
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.673
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