A Stability Analysis for Perturbed Nonlinear Iterative Methods

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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.