Displaying similar documents to “Sharp Error Bounds for Newton's Process.”

A new approach for finding weaker conditions for the convergence of Newton's method

Ioannis K. Argyros (2005)

Applicationes Mathematicae


The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the...