A posteriori error bound methods for the inclusion of polynomial zeros

Authors:
Miodrag S. Petković;Sneana Ilić;Ivan Petković
Affiliations:
Faculty of Electronic Engineering, Department of Mathematics, University of Niš, P.O. Box 73, 18000 Niš, Serbia, Serbia and Montenegro;Faculty of Science, Department of Mathematics, University of Niš, 18000 Niš, Serbia, Serbia and Montenegro;Faculty of Electronic Engineering, Department of Mathematics, University of Niš, P.O. Box 73, 18000 Niš, Serbia, Serbia and Montenegro
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

Using Carstensen's results from 1991 we state a theorem concerning the localization of polynomial zeros and derive two a posteriori error bound methods with the convergence order 3 and 4. These methods possess useful property of inclusion methods to produce disks containing all simple zeros of a polynomial. We establish computationally verifiable initial conditions that guarantee the convergence of these methods. Some computational aspects and the possibility of implementation on parallel computers are considered, including two numerical examples. A comparison of a posteriori error bound methods with the corresponding circular interval methods, regarding the computational costs and sizes of produced inclusion disks, were given.