О расширении промежутка сходимости одного обобщения метода Ньютона для решения нелинейных уравнений

А.Н. Громов
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.
doi:10.26089/nummet.v17r102 fatcat:gqmg72jidnfbncsrdbs3awdne4