Convergence of an inexact generalized Newton method with a scaled residual control

Authors:
Marek J. mietański
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

The inexact generalized Newton method is an iterative method for solving systems of nonsmooth equations. In this paper, the iterative process with a relative residual control is presented and the conditions for local convergence to a solution are provided. These results can be applied to solve Lipschitz continuous equations under some mild assumptions. Moreover, a globally convergent version of the algorithm with a damped approach based on the Armijo rule is considered.