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

Journal:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2007

Volume: 194

Issue: 2

Pages: 346-353

Type: Article

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

More publications in: Applied Mathematics and Computation

Related Projects

Diferentes tipos de condiciones iniciales para la convergencia semilocal en la aproximación de ceros de operadores no lineales. Aplicaciones.

2005/00064/001

Abstract

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.