On convergence criteria for jarratt's method

Document Type

Article

Publication Date

1-1-1984

Abstract

Let f(χ) together with its first two derivatives be continuous in the domain D and additionally let χMε{lunate}D be an extremum (or turning point) of this function. Also, let χn+1 = T (χn,χn-1,χn-2) be Jarratt's Method for computing the extremum (or turning point) of a function. Criteria are demonstrated which insure that, for any triple of initial assumptions (χ1,χ0,χ-1)ε{lunate}D, Jarratt's Method, converges to the extremum of f(χ), and that from and after some n = N0, the rate of convergence of this method increases steadily, finally becoming unbounded when the solution χM is attained. © 1984.

Identifier

0021450041 (Scopus)

Publication Title

Journal of the Franklin Institute

External Full Text Location

https://doi.org/10.1016/0016-0032(84)90023-1

ISSN

00160032

First Page

383

Last Page

401

Issue

6

Volume

317

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