On a higher order secant method.
A modified secant method is introduced for solving a nonlinear equation \(f(x)=0\). The secant of \(f(x)\) at \(x_{k}\) is replaced by a higher order approximation. It is show that this method can have quadratic convergence as the Newton method. Global monotonic convergence is proven for real functions. In Banach space, the convergence is established with relaxed Kantorovich-Ostrowski type conditions. Numerical examples confirm the conclusions.
scientific article; zbMATH DE number 1981456