A Local and Semilocal Convergence of the Continuous Analogy of Newton's Method

In this paper, a region of convergence of the continuous analogy of Newton's method is defined and an optimal choice of the parameter t is proposed. For the damped Newton's method a global convergence is proved and error bounds are obtained. The damping strategies allow one to extend the convergence domain of the initial guesses. Several damping strategies were compared. Numerical examples are given and confirm the theoretical results.

nonlinear equations in Banach spaces, damped Newton's method, recurrence relations, error bounds