A stability analysis for perturbed nonlinear iterative methods

Boggs, Paul T.; Dennis, J. E.

doi:10.1090/S0025-5718-1976-0395209-4

A stability analysis for perturbed nonlinear iterative methods
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by Paul T. Boggs and J. E. Dennis PDF

Math. Comp. 30 (1976), 199-215 Request permission

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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