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Original Articles

On a new family of simultaneous methods with corrections for the inclusion of polynomial zeros

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Pages 299-317 | Received 23 Feb 2004, Accepted 25 Mar 2006, Published online: 17 Feb 2007
 

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.

Acknowledgements

This research was supported by the Serbian Ministry of Science under grant number 144024.

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