A monotone convergence theorem for Newton-like methods using hypotheses on divided differences of order two.
Argyros, Ioannis K. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Argyros, Ioannis K. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Argyros, Ioannis K. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Argyros, Ioannis K. (1996)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Andreas Froomer (1987/88)
Numerische Mathematik
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Argyros, Ioannis K. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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José Antonio Ezquerro, Daniel González, Miguel Ángel Hernández (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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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 nonlinear integral equations of mixed Hammerstein...
Ioannis K. Argyros, Santhosh George (2013)
Applicationes Mathematicae
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We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.
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 ...
Ioannis K. Argyros (2005)
Applicationes Mathematicae
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The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich...
Argyros, Ioannis K. (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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T.J. Ypma (1984)
Numerische Mathematik
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Ioannis K. Argyros (2006)
Applicationes Mathematicae
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The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical...
Argyros, Ioannis K. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
Similarity: