A family of root-finding methods with accelerated convergence |
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Affiliation: | Faculty of Electronic Engineering University of Niš P.O. Box 73 18 000 Niš, Serbia and Montenegro |
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Abstract: | A parametric family of iterative methods for the simultaneous determination of simple complex zeros of a polynomial is considered. The convergence of the basic method of the fourth order is accelerated using Newton's and Halley's corrections thus generating total-step methods of orders five and six. Further improvements are obtained by applying the Gauss-Seidel approach. Accelerated convergence of all proposed methods is attained at the cost of a negligible number of additional operations. Detailed convergence analysis and two numerical examples are given. |
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