### A Unified Approach for Constructing Fast Two-Step Newton-like Methods.

Ioannis K. Argyros (1995)

Monatshefte für Mathematik

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Ioannis K. Argyros (1995)

Monatshefte für Mathematik

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W.M. Schmidt, Julia Mueller (1992)

Monatshefte für Mathematik

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Ioannis K. Argyros (1990)

Monatshefte für Mathematik

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Henry Brougham, Edward John Routh

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Laureano F. Escudero (1983)

Qüestiió

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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 (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...

Foltyn, Ladislav, Vlach, Oldřich

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To solve the contact problems by using a semismooth Newton method, we shall linearize stiffness and mass matrices as well as contact conditions. The latter are prescribed by means of mortar formulation. In this paper we describe implementation details.

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 Argyros (1999)

Applicationes Mathematicae

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We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative...

J. Trojan (1980)

Applicationes Mathematicae

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K. Böhmer (1981)

Numerische Mathematik

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