A Note on the Rate of Convergence of Newton's Method

Document Type

Article

Publication Date

1-1-1982

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. © 1982, Taylor & Francis Group, LLC. All rights reserved.

Identifier

84912481454 (Scopus)

Publication Title

Applicable Analysis

External Full Text Location

https://doi.org/10.1080/00036818208839409

e-ISSN

1563504X

ISSN

00036811

First Page

55

Last Page

60

Issue

1

Volume

14

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