Purely Iterative Algorithms for Newton’s Maps and General Convergence

The aim of this paper is to study the local dynamical behaviour of a broad class of purely iterative algorithms for Newton’s maps. In particular, we describe the nature and stability of fixed points and provide a type of scaling theorem. Based on those results, we apply a rigidity theorem in order t...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 7; p. 1158
Main Authors Amat, Sergio, Castro, Rodrigo, Honorato, Gerardo, Magreñán, Á. A.
Format Journal Article
LanguageEnglish
Published MDPI AG 01.07.2020
Subjects
cubic polynomials
dynamics
general convergence
Lipschitz conditions
purely iterative methods
Online AccessGet full text
ISSN2227-7390
2227-7390
DOI10.3390/math8071158

Cover

More Information
Summary:The aim of this paper is to study the local dynamical behaviour of a broad class of purely iterative algorithms for Newton’s maps. In particular, we describe the nature and stability of fixed points and provide a type of scaling theorem. Based on those results, we apply a rigidity theorem in order to study the parameter space of cubic polynomials, for a large class of new root finding algorithms. Finally, we study the relations between critical points and the parameter space.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8071158