On Steffensen�s method on Banach spaces

José Antonio Ezquerro Fernández ^[1] ; Miguel Angel Hernández Verón ^[1] ; Natalia Romero Álvarez ^[1] ; A. I. Velasco
1. [1] Universidad de La Rioja
  
  Universidad de La Rioja
  
  Logroño, España
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 249, Nº 1, 2013, págs. 9-23
Idioma: inglés
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Resumen
- We present a modification of Steffensen�s method as a predictor�corrector iterative method, so that we can use Steffensen�s method to approximate a solution of a nonlinear equation in Banach spaces from the same starting points from which Newton�s method converges.Westudy the semilocal convergence of the predictor�corrector method by using the majorant principle.Weillustrate the method with an application to a discrete problem.