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Error bounds for Newton-like methods under Kantorovich type assumptions

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Abstract

This paper provides a method for deriving newa posteriori error bounds for Newton-like methods in a Banach space under Kantorovich type assumptions. The bounds found are sharper than those of Miel [10] and include those recently obtained by Moret [12]. The applicability of our method is studied for other types of iterations including Newton’s method.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ehime University, 790, Matsuyama, Japan

    Tetsuro Yamamoto

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  1. Tetsuro Yamamoto
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Additional information

This research was done while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, U.S.A. from March 29, 1985 to October 21, 1985.

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Yamamoto, T. Error bounds for Newton-like methods under Kantorovich type assumptions. Japan J. Appl. Math. 3, 295–313 (1986). https://doi.org/10.1007/BF03167104

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  • DOI: https://doi.org/10.1007/BF03167104

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