Newton's Method Under Mild Differentiability Conditions with Error Analysis.
J. Rokne (1971/72)
Numerische Mathematik
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J. Rokne (1971/72)
Numerische Mathematik
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P. LANCASTER (1966/67)
Numerische Mathematik
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Tetsuro Yamamoto (1986)
Numerische Mathematik
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F.A. Potra, V. Pták (1980)
Numerische Mathematik
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Peter Wilhelm Meyer (1984)
Numerische Mathematik
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Tetsuro Yamamoto (1986)
Numerische Mathematik
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H.C. Lai, P.Y. Wu (1982)
Numerische Mathematik
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A.A. GOLDSTEIN (1965)
Numerische Mathematik
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O.H. Hald (1974/75)
Numerische Mathematik
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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...
José Antonio Ezquerro, Daniel González, Miguel Ángel Hernández (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to ...