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Computational Aspects of the Implementation of Disk Inversions

More than three decades the implementation of iterative methods for the simultaneous inclusion of polynomial zeros in circular complex interval arithmetic is carried out using the exact inversion of disks. Based on theoretical analysis and numerical examples, we show that the centered inversion gives smaller inclusion disks. This surprising result is the consequence of better convergence of the midpoints of produced disks when the centered inversion is employed. Some examples of inclusion methods with the centered and exact inversion, together with numerical results, are given.