Local convergence theorems for Newton's method from data at one point

Volume 29 / 2002

Ioannis K. Argyros Applicationes Mathematicae 29 (2002), 481-486 MSC: 65B05, 47H17, 49D15, 65G99, 65J15, 65N30, 65N35. DOI: 10.4064/am29-4-7


We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.


  • Ioannis K. ArgyrosDepartment of Mathematics
    Cameron University
    Lawton, OK 73505, U.S.A.

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