An acceleration of Newton's method: Super-Halley method

  1. Gutiérrez, J.M. 1
  2. Hernández, M.A. 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: 2001

Volume: 117

Issue: 2

Pages: 223-239

Type: Article

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DOI: 10.1016/S0096-3003(99)00175-7 SCOPUS: 2-s2.0-0040927500 WoS: WOS:000166352000008 GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

From a study of the convexity we give an acceleration for Newton's method and obtain a new third order method. Then we use this method for solving non-linear equations in Banach spaces, establishing conditions on convergence, existence and uniqueness of solution, as well as error estimates © 2001 Elsevier Science Inc.