Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton’s maps

Gerardo Honorato and Sergio Plaza

Applied Mathematics and Computation, 2015, vol. 251, issue C, 507-520

Abstract: In this paper we define purely iterative algorithm for Newton’s maps which is a slight modification of the concept of purely iterative algorithm due to Smale. For this, we use a characterization of rational maps which arise from Newton’s method applied to complex polynomials. We prove the Scaling Theorem for purely iterative algorithm for Newton’s map. Then we focus our study in dynamical aspects of three root-finding iterative methods viewed as a purely iterative algorithm for Newton’s map: Whittaker’s iterative method, the super-Halley iterative method and a modification of the latter. We give a characterization of the attracting fixed points which correspond to the roots of a polynomial. Also, numerical examples are included in order to show how to use the characterization of fixed points. Finally, we give a description of the parameter spaces of the methods under study applied to a one-parameter family of generic cubic polynomials.

Keywords: Whittaker’s iterative method; The super-Halley iterative method; Dynamics; Rational maps; Conjugacy classes (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314016154
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:507-520

DOI: 10.1016/j.amc.2014.11.083

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().