Methods with prefixed order for approximating square roots with global and general convergence.

  1. Hernández, M.A. 1
  2. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2007

Volumen: 194

Número: 2

Páginas: 346-353

Tipo: Artículo

DOI: 10.1016/J.AMC.2007.04.033 SCOPUS: 2-s2.0-36048940727 WoS: WOS:000253496000006 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

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Resumen

A family of Newton-like methods is constructed to approximate the square root of a positive real number. The iterative methods of the family are global or generally convergent depending on the prefixed order of convergence is even or odd. We show the dynamical behaviour of some of these methods by means of several Julia sets and the intricate fractal structures which arise from the order of the iterative methods are displayed. © 2007 Elsevier Inc. All rights reserved.