FINDING GOOD STARTING POINTS FOR SOLVING EQUATIONS BY NEWTON'S METHOD

Ioannis Argyros
2009 Rev. Anal. Numér. Théor. Approx   unpublished
We study the problem of finding good starting points for the semilo-cal convergence of Newton's method to a locally unique solution of an operator equation in a Banach space setting. Using a weakened version of the Newton-Kantorovich theorem we show that the procedure suggested by Kung [6] is improved in the sense that the number of Newton-steps required to compute a good starting point can be significantly reduced (under the same computational cost required in the Newton-Kantorovich theorem
more » ... torovich theorem [3], [5]). MSC 2000. 65H10, 65G99, 47H17, 49M15.
fatcat:4vwxqkc2u5h2vayauupfihr47q