Semilocal Convergence of the Secant Method under Mild Convergence Conditions of Differentiability

  1. Hernández, M.A. 1
  2. Rubio, M.J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Computers & Mathematics with Applications

ISSN: 0898-1221

Año de publicación: 2002

Volumen: 44

Número: 3-4

Páginas: 277-285

Tipo: Artículo

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DOI: 10.1016/S0898-1221(02)00147-5 SCOPUS: 2-s2.0-0036681220 WoS: WOS:000176539600001 GOOGLE SCHOLAR

Otras publicaciones en: Computers & Mathematics with Applications

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Resumen

In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder continuous conditions. Also, we obtain a result for uniqueness of solutions. © 2002 Elsevier Science Ltd. All rights reserved.