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A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators

Volume 42 / 2015

I. K. Argyros, D. González Applicationes Mathematicae 42 (2015), 29-56 MSC: 65G99, 65J15, 49M15, 47J25, 47J05. DOI: 10.4064/am42-1-4


We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.


  • I. K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • D. GonzálezCenter on Mathematical Modelling
    Escuela Politécnica Nacional
    Quito, Ecuador

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