Schröder-like Methods for the Simultaneous Inclusion of Polynomial Zeros

The subject of this paper is the study of Schröder-like methods for the simultaneous inclusion of multiple complex zeros of a polynomial in circular complex arithmetic. These methods are based on the fundamental work of Gargantini and Henrici [7] and belong to the class of the most efficient inclusion methods. Apart from a review of the existing methods of Schröder’s type, together with their convergence properties, a new, accelerated method in serial (single-step) mode with Schröder’s correction is proposed. The comparison of the considered methods based on their computational efficiency and numerical results are given.