A convergence theorem for Newton-like methods in Banach spaces
Numerische Mathematik
Convergence of Newton-like methods for singular operator equations using outer inverses
Numerische Mathematik
A discretization scheme for some conservative problems
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
On the R-order of convergence of Newton's method under mild differentiability conditions
Journal of Computational and Applied Mathematics
On the weakening of the convergence of Newton's method using recurrent functions
Journal of Complexity
Extending the Newton-Kantorovich hypothesis for solving equations
Journal of Computational and Applied Mathematics
Weaker conditions for the convergence of Newton's method
Journal of Complexity
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Newton-like methods are often used for solving nonlinear equations. In the present paper, we introduce very general majorizing sequences for Newton-like methods. Then, we provide semi-local convergence results for these methods. The new convergence results can be weaker than in earlier studies. These new results are illustrated by several numerical examples and special cases of Newton-like methods, for which the older convergence conditions do not hold but for which our weaker convergence conditions are satisfied.