Author： Petković M. Milošević D.
Publisher： Taylor & Francis Ltd
ISSN： 0020-7160
Source： International Journal of Computer Mathematics, Vol.83, Iss.3, 2006-03, pp. : 299-317
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Abstract
A high-order one-parameter family of inclusion methods for the simultaneous inclusion of all simple complex zeros of a polynomial is presented. For specific values of the parameter, some known interval methods are obtained. The convergence rate of the basic fourth-order family is increased to 5 and 6 using Newton's and Halley's corrections, respectively. Using the concept of the R -order of convergence of mutually dependent sequences, we present a convergence analysis of the accelerated total-step and single-step methods with corrections. The suggested inclusion methods have great computational efficiency since an increase of the convergence rate is attained with only a few additional calculations. Two numerical examples are included to demonstrate the convergence properties of the proposed methods.
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