Globally convergent algorithm for solving nonlinear equations

A general iterative method is proposed for finding the maximal rootx_max of a one-variable equation in a given interval. The method generates a monotone-decreasing sequence of points converging tox_max or demonstrates the nonexistence of a real root. It is globally convergent. A concrete realization of the general algorithm is also given and is shown to be locally quadratically convergent. Computational experience obtained for eight test problems indicates that the new method is comparable to known methods claiming global convergence.