Abstract
In this paper, applying the majorant function method, we present a new proof of the convergence of the Durand-Kerner method, and obtain a greater computable radius estimation of safe initial discs. This result is an improvement of all results now available. Furthermore, combining the Kuhn algorithm for solving all zeros of polynomials, we obtain a discriminant to get safe initial discs. Finally, we compare the complexity between the Durand-Kerner algorithm and several known results, and the numerical results show the superiority of our result.
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