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A convergence theorem for Newton-like methods in Banach spaces

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A convergence theorem for Newton-like methods in Banach spaces is given, which improves results of Rheinboldt [27], Dennis [4], Miel [15, 16] and Moret [18] and includes as a special case an updated (affine-invariant [6]) version of the Kantorovich theorem for the Newton method given in previous papers [35, 36]. Error bounds obtained in [34] are also improved. This paper unifies the study of finding sharp error bounds for Newton-like methods under Kantorovich type assumptions.

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Sponsored by the United States Army under Contract No. DAAG29-80-C-0041 and by the Ministry of Education, Japan

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Yamamoto, T. A convergence theorem for Newton-like methods in Banach spaces. Numer. Math. 51, 545–557 (1987). https://doi.org/10.1007/BF01400355

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