Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.
Tetsuro Yamamoto (1986)
Numerische Mathematik
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Displaying similar documents to “A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.”
Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.
Unified Error Analysis for Newton-Type Methods .
G.J. Miel (1979)
Numerische Mathematik
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Error bounds for Newton's method under a weak Kantorovich-type hypothesis.
Argyros, Ioannis K. (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Newton's Method Under Mild Differentiability Conditions with Error Analysis.
J. Rokne (1971/72)
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Sharp Error Bounds for Newton's Process.
F.A. Potra, V. Pták (1980)
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Error Bounds of Newton Type Process on Banach Spaces.
H.C. Lai, P.Y. Wu (1982)
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Error Analysis for the Newton-Raphson Method.
P. LANCASTER (1966/67)
Numerische Mathematik
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A new approach for finding weaker conditions for the convergence of Newton's method
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...
Das modifizierte Newton-Verfahren in verallgemeinerten Banach-Räumen.
Peter Wilhelm Meyer (1984)
Numerische Mathematik
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A Convergence Theorem for Newton-Like Methods in Banach Spaces.
Tetsuro Yamamoto (1987)
Numerische Mathematik
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A unifying semilocal convergence theorem for Newton-like methods in Banach space.
Argyros, Ioannis K.I. (1998)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
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 ...