Abstract
We approximate a locally unique solution of an equation on a Banach space setting using Newton’smethod.Motivated by the work by Ferreira and Svaiter [5] but using more precise majorization sequences, and under the same computational cost we provide: a larger convergence region; finer error bounds on the distances involved, and an at least as precise information on the location of the solution than in [5]. The results can also compare favorably to the corresponding ones given byWang in [10]. Finally we complete the study with two concrete applications.
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Argyros, I.K. Concerning the semilocal convergence of Newton’s method and convex majorants. Rend. Circ. Mat. Palermo 57, 331–341 (2008). https://doi.org/10.1007/s12215-008-0024-5
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DOI: https://doi.org/10.1007/s12215-008-0024-5