Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65H10, 90C30

Retrieve articles in all journals with MSC: 65H10, 90C30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1990-1023050-5
PII: S 0025-5718(1990)1023050-5
Keywords: Nonlinear simultaneous equations, Least Change Secant Updates, quasi-Newton methods, Inexact Newton methods
Article copyright: © Copyright 1990 American Mathematical Society