Convergence of Newton’s method under the gamma condition

Ioannis K. Argyros

Resumen


We provide a semilocal as well as a local convergence analysis of Newton’s method using the gamma condition [1], [10], [11]. Using more precise majorizing sequences than before [4], [8]—[11] and under at least as weak hypotheses, we provide in the semilocal case: finer error bounds on the distances involved and an at least as precise information on the location of the solution; in the local case: a larger radius of convergence.

Palabras clave


Banach space; Newton’s method; local/semilocal convergence; Newton—Kantorovich theorem; Frechet derivative; majorizing sequence; radius of convergence; gamma condition; analytic operator; espacio de Banach; método de Newton; convergencia local/semilocal.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172006000300006

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