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Mathematics of Computation

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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
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1976-0395209-4
Keywords: Nonlinear iterative methods, stability analysis, consistent approximations, steepest descent, Newton's method, nonlinear least squares methods
Article copyright: © Copyright 1976 American Mathematical Society