Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



A stability analysis for perturbed nonlinear iterative methods

Authors: Paul T. Boggs and J. E. Dennis
Journal: Math. Comp. 30 (1976), 199-215
MSC: Primary 65H10
MathSciNet review: 0395209
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper applies the asymptotic stability theory for ordinary differential equations to Gavurin’s continuous analogue of several well-known nonlinear iterative methods. In particular, a general theory is developed which extends the Ortega-Rheinboldt concept of consistency to include the widely used finite-difference approximations to the gradient as well as the finite-difference approximations to the Jacobian in Newton’s method. The theory is also shown to be applicable to the Levenberg-Marquardt and finite-difference Levenberg-Marquardt methods.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65H10

Retrieve articles in all journals with MSC: 65H10

Additional Information

Keywords: Nonlinear iterative methods, stability analysis, consistent approximations, steepest descent, Newton’s method, nonlinear least squares methods
Article copyright: © Copyright 1976 American Mathematical Society