A family of root-finding methods with accelerated convergence

Authors:
M. S. Petkovi;L. Z. Rani
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 8
Cited 1

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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.