Analytical View of Sir Isaac Newton's Principia
Henry Brougham, Edward John Routh
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Henry Brougham, Edward John Routh
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Laureano F. Escudero (1983)
Qüestiió
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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.
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...
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...
Yan Gao (2001)
Applications of Mathematics
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The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since...
Aleksandar Lipkovski (1988)
Mathematische Zeitschrift
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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 ...
Dontchev, Asen (1996)
Serdica Mathematical Journal
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* This work was supported by National Science Foundation grant DMS 9404431. In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that...