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 and, second, it improves the
results obtained through majorizing sequences. In addition, the authors extend the application of Newton's method in Banach
spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich's theory for Newton's
method is substantially broadened. Moreover, this technique can be applied to any iterative method.
This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists
in general with an interest in numerical analysis.