Mild Differentiability Conditions for Newton's Method in Banach Spaces (eBook, PDF)

Mild Differentiability Conditions for Newton's Method in Banach Spaces (eBook, PDF)

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In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors' technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich's majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type...

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