A note on the rate of convergence of newton's method

Abstract

The rate of convergence concept introduced by D. Young in the analysis of linear iterative procedures is extended to include iterative methods for solving nonlinear problems by introducing a rate of convergence measure defined for each step of the iterative computation. This new concept includes previously known asymptotic results as the limit of a sequence. This new formulation is applied to Newton's Method and it is demonstrated that its rate of convergence increases in magnitude if not at each step of the computation at least it increases steadily from and after some step of the computation.

AMS(MOS) 65H10

C.R. Classification 5.15

Additional information

Notes on contributors

Hamilton Chase

H. J. Töpfer