Abstract:
An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton's method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations.
Keywords:iterative processes, Newton's method, logarithmic derivative, continuous functions defined on a segment, higher order methods, interval of convergence, transcendental equations.