A COMPARATIVE STUDY BETWEEN CONVERGENCE RESULTS FOR NEWTON'S METHOD

  • Argyros, Ioannis K. (CAMERON UNIVERSITY, DEPARTMENT OF MATHEMATICS SCIENCES) ;
  • Hilout, Said (POITIERS UNIVERSITY, LABORATOIRE DE MATHEMATIQUES ET APPLICATIONS)
  • Published : 2008.11.30

Abstract

We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.