An improved convergence analysis of Newton's method for twice Fréchet differentiable operators

Volume 40 / 2013

Ioannis K. Argyros, Sanjay K. Khattri Applicationes Mathematicae 40 (2013), 459-481 MSC: Primary 65-XX, 47Hxx, 49Mxx; Secondary 65J20, 65B05, 65G99, 65J15, 65N30, 65N35, 65H10, 47H17, 49M15. DOI: 10.4064/am40-4-6


We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505-6377, U.S.A.
  • Sanjay K. KhattriDepartment of Engineering
    Stord/Haugesund University College
    N-414 Stord, Norway

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