The convergence of the perturbed Newton method and its application for ill-conditioned problems

The convergence of the perturbed Newton method and its application for ill-conditioned problems

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Article ID: iaor201110691
Volume: 218
Issue: 7
Start Page Number: 2988
End Page Number: 3001
Publication Date: Dec 2011
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: Newton method
Abstract:

Iterative methods, such as Newton’s, behave poorly when solving ill‐conditioned problems: they become slow (first order), and decrease their accuracy. In this paper we analyze deeply and widely the convergence of a modified Newton method, which we call perturbed Newton, in order to overcome the usual disadvantages Newton’s one presents. The basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization. Choices for that parameter are proposed. The theoretical analysis will be illustrated through examples.

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