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Mathematics of Computation

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Local convergence theory of inexact Newton methods based on structured least change updates

Author: José Mario Martínez
Journal: Math. Comp. 55 (1990), 143-167
MSC: Primary 65H10; Secondary 90C30
MathSciNet review: 1023050
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Abstract: In this paper we introduce a local convergence theory for Least Change Secant Update methods. This theory includes most known methods of this class, as well as some new interesting quasi-Newton methods. Further, we prove that this class of LCSU updates may be used to generate iterative linear methods to solve the Newton linear equation in the Inexact-Newton context. Convergence at a q-superlinear rate (or at an "ideal" linear rate, in the sense of Dennis-Walker) of the Inexact Newton methods generated in this way is proved, independently of the number of iterations used in the linear iterative subalgorithm. We apply the new theory to some particular methods.

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Keywords: Nonlinear simultaneous equations, Least Change Secant Updates, quasi-Newton methods, Inexact Newton methods
Article copyright: © Copyright 1990 American Mathematical Society