On the Newton-like Method for the Inclusion of a Polynomial Zero

One of the most important problems in solving nonlinear equations is the construction of such initial conditions which provide both the guaranteed and fast convergence of the considered numerical algorithms. In this paper we study an iterative method of Newton’s type for the inclusion of isolated complex zero of a given polynomial. We state computationally verifiable initial condition for the convergence of the considered interval method, which depends only on attainable data, and prove the quadratic convergence of this method. A numerical example is given.