Displaying similar documents to “Inverse differentiability contractors and equations in Banach spaces”

Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses

Ioannis K. Argyros (2000)

Czechoslovak Mathematical Journal

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We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems,...

Continuity of the Drazin inverse II

J. Koliha, V. Rakočević (1998)

Studia Mathematica

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We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

A new Kantorovich-type theorem for Newton's method

Ioannis Argyros (1999)

Applicationes Mathematicae

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A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.