Dynamics of the King and Jarratt iterations View Full Text


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Article Info

DATE

2005-05

AUTHORS

Sergio Amat, Sonia Busquier, Sergio Plaza

ABSTRACT

Summary.The purpose of this article is to present results that amount to a description of the conjugacy classes of two fourth-order root-finding iterative methods, namely King’s family of iterative methods and Jarratt’s iterative method, for complex polynomials of degrees 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 families, 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 polyno- mial having the same degree. For degree four, partial results analogous to the ones just described are presented. More... »

PAGES

212-223

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00010-004-2733-y

DOI

http://dx.doi.org/10.1007/s00010-004-2733-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1039772729


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