Dynamics of the King and Jarratt iterations

• Autores: Sergio Amat Plata , Sonia Busquier Sáez , Sergio Plaza Salinas
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 69, Nº. 3, 2005, págs. 212-223
• Idioma: inglés
• DOI: 10.1007/s00010-004-2733-y
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• Resumen

  • 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 Kings family of iterative methods and Jarratts 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.