Une variante de la méthode de Newton: A variant of the Newton method - Păvăloiu, Ion (Anal. Numér. Théor. Approx., 1978)
Let \(X\) be a Banach space, \(Y\) a normed space, \(P:X→ Y\) a nonlinear operator and the equation \(P( x) =0\). The first order derivative is approximated by the partial derivative of an operator of two variables, whose diagonal restrictive coincides with \(P\). We give a semilocal convergence result for the considered method.