A family of iterative methods that uses divided differences of first and second orders

  1. Ezquerro, J.A. 2
  2. Grau-Sánchez, M. 1
  3. Hernández-Verón, M.A. 2
  4. Noguera, M. 1
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Zeitschrift:
Numerical Algorithms

ISSN: 1017-1398

Datum der Publikation: 2015

Ausgabe: 70

Nummer: 3

Seiten: 571-589

Art: Artikel

DOI: 10.1007/S11075-015-9962-0 SCOPUS: 2-s2.0-84945479019 WoS: WOS:000363268900007 GOOGLE SCHOLAR

Andere Publikationen in: Numerical Algorithms

Projekte im Zusammenhang

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

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

2012/00014/001

Zusammenfassung

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592–9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.