• Title/Summary/Keyword: radius of convergence$H{\ddot{o}}lder$ continuity

Search Result 2, Processing Time 0.016 seconds

LOCAL CONVERGENCE OF THE SECANT METHOD UPPER $H{\ddot{O}}LDER$ CONTINUOUS DIVIDED DIFFERENCES

  • Argyros, Ioannis K.
    • East Asian mathematical journal
    • /
    • v.24 no.1
    • /
    • pp.21-25
    • /
    • 2008
  • The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

  • PDF

ON THE RADIUS OF CONVERGENCE OF SOME NEWTON-TYPE METHODS IN BANACH SPACES

  • Argyros, Ioannis K.;Hilout, Said
    • The Pure and Applied Mathematics
    • /
    • v.18 no.3
    • /
    • pp.219-230
    • /
    • 2011
  • We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.