RATE OF CONVERGENCE OF A GENERALIZATION OF NEWTON METHOD

Authors
BENADADA Y CROUZEIX JP FERLAND JA
Citation
Y. Benadada et al., RATE OF CONVERGENCE OF A GENERALIZATION OF NEWTON METHOD, Journal of optimization theory and applications, 78(3), 1993, pp. 599-604
Citations number
4
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
Journal title
Journal of optimization theory and applications → ACNP
ISSN journal
00223239
Volume
78
Issue
3
Year of publication
1993
Pages
599 - 604
Database
ISI
SICI code
0022-3239(1993)78:3<599:ROCOAG>2.0.ZU;2-1
Abstract
The Newton's method for finding the root of the equation THETA(t) = 0 can be easily generalized to the case where THETA is monotone, convex, but not differentiable. Then, the convergence is superlinear. The pur pose of this note is to show that the convergence is only superlinear. Indeed, for all alpha is-an-element-of (1, 2), we exhibit an example where the convergence of the iterates is exactly alpha.