𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On convergence criteria for jarratt's method

✍ Scribed by H.A. Chase

Book ID
103086710
Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
1020 KB
Volume
317
Category
Article
ISSN
0016-0032

No coin nor oath required. For personal study only.

✦ Synopsis

Let f(x) together with itsJirst two derivatives be continuous in the domain D and additionally let xlrl E D be an extremum (or turning point) of this function. Also, let x,, + , = T (x,, x,, _ , , xn _ J 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 (xl, x0, x_ i) E D, Jarratt's Method, converges to the extremum off(x), and that from and after some n = N,, the rate of convergence of this method increases steadily, jnally becoming unbounded when the solution x,, is attained.

πŸ“œ SIMILAR VOLUMES

A new convergence theorem for the Jarrat
A new convergence theorem for the Jarratt method in Banach space
✍ I.K. Argyros πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 340 KB

In this study, we approximate a locally unique solution of a nonlinear equation in Banach space using the Jarratt method. Sufficient convergence conditions for this method have already been given by several authors, when the equation is defined on the real line, or complex plane [1-3], or in Banach