Extending the applicability of the local and semilocal convergence of Newton's method
Argyros, Ioannis K
Magreñán, Á. Alberto (1)
Tipo de Ítem:Articulo Revista Indexada
We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: local case: a larger radius is given as well as more precise error estimates on the distances involved. Semilocal case: the convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results.
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