On a new method for enlarging the radius of convergence for Newton's method

Volume 28 / 2001

Ioannis K. Argyros Applicationes Mathematicae 28 (2001), 1-15 MSC: 65B05, 47H17, 49D15. DOI: 10.4064/am28-1-1


We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the $m$th-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.


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

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