### A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.

Tetsuro Yamamoto (1986)

Numerische Mathematik

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Tetsuro Yamamoto (1986)

Numerische Mathematik

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G.J. Miel (1979)

Numerische Mathematik

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H.C. Lai, P.Y. Wu (1982)

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J. Rokne (1971/72)

Numerische Mathematik

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Tetsuro Yamamoto (1986)

Numerische Mathematik

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P. LANCASTER (1966/67)

Numerische Mathematik

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Argyros, Ioannis K. (2002)

Southwest Journal of Pure and Applied Mathematics [electronic only]

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O.H. Hald (1974/75)

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Peter Wilhelm Meyer (1984)

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A.A. GOLDSTEIN (1965)

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Ioannis K. Argyros (2005)

Applicationes Mathematicae

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The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the...