How to apply Newton's method to operators with unbounded second derivative

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Livre:
AIP Conference Proceedings

ISBN: 978-073540956-9

Année de publication: 2011

Volumen: 1389

Pages: 1046-1048

Type: Chapitre d'ouvrage

DOI: 10.1063/1.3637790 SCOPUS: 2-s2.0-81855184392 WoS: WOS:000302239800255 GOOGLE SCHOLAR

Résumé

The problem of finding the roots of a nonlinear equation has a long history. Although some nonlinear equations can be solved analytically, numerical approximations of the roots can be normally wanted. Moreover, since it is usually difficult or impossible to obtain an exact root of a nonlinear equation, we usually have to be satisfied with approximating the root numerically. To do this, we habitually approximate the root by iterative methods, which provide a sequence of approximations, from one or several initial approximations, that converges to the root of the nonlinear equation. © 2011 American Institute of Physics.