A local convergence theorem for the inexact Newton method at singular points.
Argyros, Ioannis K. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Displaying similar documents to “Convergence of Newton-like methods for singular operator equations using outer inverses.”
A local convergence theorem for the inexact Newton method at singular points.
On Newton-Like Methods.
J.E. jr. DENNIS (1968)
Numerische Mathematik
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Sublinear Convergence of the Chord Method at Singular Points.
D.W. Decker, C.T. Kelley (1983)
Numerische Mathematik
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Convergence of Newton-Like-Iterative Methods.
T.J. Ypma (1984)
Numerische Mathematik
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Newton's Method for Gradient Equations Based upon the Fixed Point Map: Convergence and Complexity Study.
Joseph W. Jerome (1987)
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 convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
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...
Convergence of the Newton Process to Multiple Solutions.
L.B. RALL (1966/67)
Numerische Mathematik
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Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses.
Argyros, Ioannis K. (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Semilocal convergence for Newton's method on a Banach space with a convergence structure and twice Fréchet differentiable operators.
Argyros, Ioannis K. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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A Kantorovich-type Convergence Analysis for the Gauss-Newton-Method.
W.M. Häußler (1986)
Numerische Mathematik
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New unifying convergence criteria for Newton-like methods
Ioannis K. Argyros (2002)
Applicationes Mathematicae
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We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence...
On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations
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.
Convergence of Newton-Like Methods for Solving Systems of Nonlinear Equations.
J.C.P. Bus (1976/1977)
Numerische Mathematik
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