Newton's method and regularly smooth operators
DOI:
https://doi.org/10.33993/jnaat401-946Keywords:
Newton's method, Banach space, majorizing sequence, regularly smooth operators, Fréchet-derivative, semilocal convergence, integral equation, radiative transfer, Newton-Kantorovich hypothesisAbstract
A semilocal convergence analysis for Newton's method in a Banach space setting is provided in this study. Using a combination of regularly smooth and center regularly smooth conditions on the operator involved, we obtain more precise majorizing sequences than in [7]. It then follows that under the same computational cost and the same or weaker hypotheses than in [7] the following benefits are obtained: larger convergence domain; finer estimates on the distances involved, and an at least as precise information on the location of the solution of the corresponding equation. Numerical examples are given to further validate the results obtained in this study.Downloads
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