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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A theory of secant preconditioners


Author: José Mario Martínez
Journal: Math. Comp. 60 (1993), 681-698
MSC: Primary 65H10
MathSciNet review: 1176714
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Abstract: In this paper we analyze the use of structured quasi-Newton formulae as preconditioners of iterative linear methods when the inexact-Newton approach is employed for solving nonlinear systems of equations. We prove that superlinear convergence and bounded work per iteration is obtained if the preconditioners satisfy a Dennis-Moré condition. We develop a theory of Least-Change Secant Update preconditioners and we present an application concerning a structured BFGS preconditioner.


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DOI: https://doi.org/10.1090/S0025-5718-1993-1176714-X
Keywords: Nonlinear systems, inexact-Newton methods, quasi-Newton methods, preconditioners
Article copyright: © Copyright 1993 American Mathematical Society