On the improved family of simultaneous methods for the inclusion of multiple polynomial zeros

Dušan M. Milošević, Ljiljana D. Petković

Starting from a family of iterative methods for the simultaneous inclusion of multiple complex zeros, we construct efficient iterative methods with accelerated convergence rate by the use of Gauss-Seidel procedure and the suitable corrections. The proposed methods are realized in the circular complex interval arithmetic and produce disks that contain the wanted zeros. The suggested algorithms possess a high computational efficiency since the increase of the convergence rate is attained without additional calculations. Using the concept of the $R$-order of convergence of mutually dependent sequences, the convergence analysis of the proposed methods is presented. Numerical results are given to demonstrate the convergence properties of the considered methods.