A note on the Kantorovich theorem for Newton iteration
The paper discusses the convergence of the Newton method for a nonsingular solution of the nonlinear equation \(f(x) = 0\) with \(f: X \to Y\) two times differentiable and \(X\), \(Y\) are Banach spaces. Based on the information of the second derivatives of \(f\) at the initial point, the author gives a new criterion for the convergence of the Newton iteration.
scientific article; zbMATH DE number 428536