A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
Tetsuro Yamamoto (1986)
Numerische Mathematik
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Displaying similar documents to “Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.”
A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
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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Sharp Error Bounds for Newton's Process.
F.A. Potra, V. Pták (1980)
Numerische Mathematik
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Unified Error Analysis for Newton-Type Methods .
G.J. Miel (1979)
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...
Newton's Method Under Mild Differentiability Conditions with Error Analysis.
J. Rokne (1971/72)
Numerische Mathematik
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Error Bounds of Newton Type Process on Banach Spaces.
H.C. Lai, P.Y. Wu (1982)
Numerische Mathematik
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Error Analysis for the Newton-Raphson Method.
P. LANCASTER (1966/67)
Numerische Mathematik
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On Calculating the Eigenvalues of the Finite Hill's Differential Equation
E. Wagenführer (1983)
Numerische Mathematik
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On Ostrowski's fundamental existence theorem.
M.D. Presic (1978)
Publications de l'Institut Mathématique [Elektronische Ressource]
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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 ...