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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- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 199-215
- MSC: Primary 65H10
- DOI: https://doi.org/10.1090/S0025-5718-1976-0395209-4
- MathSciNet review: 0395209