Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Dynamics of the King and Jarratt The purpose of this article is to present results that amount to a de
 

Summary: Dynamics of the King and Jarratt
iterations
The purpose of this article is to present results that amount to a de­
scription of the conjugacy classes of two forth--order root--finding iterative
methods, the King and the Jarratt iterations, for complex polynomials of de­
grees two, three and four. For degrees two and three, a full description of the
conjugacy classes is accomplished, in each case, by a one--parameter family of
polynomials. This is done in such a way that, when one applies one of these
two root--finding iterative methods to the elements of these parametrized fam­
ilies, a family of iterative methods is obtained, and its dynamics represents,
up to conjugacy, the dynamics of the corresponding iterative root--finding
method applied to any complex polynomial having the same degree. For de­
gree four, partial results analogous to the ones just described are presented.
Key Words. King and Jarratt iterative methods, dynamics, rational
maps, conjugacy classes.
AMS(MOS) subject classifications. 37N30, 65F10, 30C15.
1

  

Source: Amat, Sergio - Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena

 

Collections: Mathematics