Improved methods for the simultaneous inclusion of multiple polynomial zeros

Using a new fixed point relation, the interval methods for the simultaneous inclusion of complex multiple zeros in circular complex arithmetic are constructed. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Schroder's and Halley-like corrections under computationally verifiable initial conditions. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Two numerical examples are given to demonstrate convergence characteristics of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.