On some iterative methods for solving nonlinear equations. (English) Zbl 0818.65050

The paper is devoted to the study of nonlinear equations of the form \(f(x) + g(x) = 0\) in Banach spaces, with \(f\) a differentiable operator and \(g\) a nondifferentiable but continuous operator. The main idea is to replace the first derivative of \(g\) in the classical Newton method – which cannot be applied here – by the first-order divided difference of \(g\). The obtained method consisting of a combination of Newton and chord methods has the same order of convergence as the chord method. A numerical example is also given.


65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators