On a second order method for the simultaneous inclusion of polynomial complex zeros in rectangular arithmetic

Starting from separated rectangles in the complex plane which contain polynomial complex zeros, an iterative method of second order for the simultaneous inclusion of these zeros is formulated in rectangular arithmetic. The convergence and a condition for convergence are considered. Applying Gauss-Seidel approach to the proposed method, two accelerated interval methods are formulated. TheR-order of convergence of these methods is determined. An analysis of the convergence order is given in the presence of rounding errors. The presented methods are illustrated numerically in examples of polynomial equations.