On the Improved Family of Simultaneous Methods for the Inclusion of Multiple Polynomial Zeros
نویسندگان
چکیده
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. AMS Mathematical Subject Classification (1991): 65H05, 65G20, 30C15.
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