Convergence and Complexity of Newton Iteration for Operator Equations

@article{Traub1979ConvergenceAC,
title={Convergence and Complexity of Newton Iteration for Operator Equations},
author={J. Traub and H. Wozniakowski},
journal={J. ACM},
year={1979},
volume={26},
pages={250-258}
}

Abstract : An optimal convergence condition for Newton iteration in a Banach space is established. There exist problems for which the iteration converges but the complexity is unbounded. It is shown which stronger condition must be imposed to also assure good complexity.