A general semilocal convergence result for Newton’s method under centered conditions for the second derivative

  1. Ezquerro, J.A. 1
  2. González, D. 1
  3. Hernández, M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Zeitschrift:
Mathematical Modelling and Numerical Analysis

ISSN: 0764-583X

Datum der Publikation: 2013

Ausgabe: 47

Nummer: 1

Seiten: 149-167

Art: Artikel

DOI: 10.1051/M2AN/2012026 SCOPUS: 2-s2.0-84996129118 WoS: WOS:000313646300007 GOOGLE SCHOLAR

Andere Publikationen in: Mathematical Modelling and Numerical Analysis

Institutionelles Repository: lock_openOpen Access Editor

Projekte im Zusammenhang

Procesos iteratios para resolver ecuaciones no lineales: construcción, convergencia, eficacia, análisis dinámico y aplicaciones

2012/00014/001

Zusammenfassung

From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type