Kantorovich's Majorants Principle for Newton's Method

Orizon Ferreira (orizonmat.ufg.br)
Benar Svaiter (benarimpa.br)

Abstract: We prove Kantorovich's theorem on Newton's method using a convergence analysis which makes clear, with respect to Newton's Method, the relationship of the majorant function and the non-linear operator under consideration. This approach enable us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results.

Keywords: Kantorovich theorem, Newton method , AMSC: 49M15, 90C30

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: Série A do IMPA- A429 / 2006.

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Entry Submitted: 01/23/2006
Entry Accepted: 01/23/2006
Entry Last Modified: 01/23/2006

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