On the simultaneous improving k inclusion disks for polynomial zeros

A modification of the iterative method of Borsch-Supan type for the si- multaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of k (of n ‚ k) zeros, dealing with k inclu- sion disks of these zeros and the point (unchangeable) approximations to the remaining nik zeros. It is proved that the R-order of convergence of the con- sidered method is two if k < n and three if k = n. Three numerical examples are given to illustrate convergence properties of the presented method.