On the Domain of Starting Points of Newton’s Method Under Center Lipschitz Conditions

  1. Ezquerro, J.A. 1
  2. Hernández-Verón, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Mediterranean Journal of Mathematics

ISSN: 1660-5446

Year of publication: 2015

Volume: 13

Issue: 4

Pages: 2287

Type: Article

DOI: 10.1007/S00009-015-0596-1 SCOPUS: 2-s2.0-84931087146 WoS: WOS:000380671700057 GOOGLE SCHOLAR

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Abstract

When the semilocal convergence of Newton’s method is studied in Banach spaces under center Lipschitz conditions, it is usual to choose the point where the Lipschitz condition is centered as the initial point for Newton’s method. In this work, we improve this choice looking for a domain of initial points (a convergence domain). © 2015 Springer Basel