A class of higher order algorithms for computing polynomial zeros

Mohammed A. Hasan

doi:10.1109/CDC.2005.1583217

A class of higher order algorithms for computing polynomial zeros

Mohammed A. Hasan

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

A general framework for deriving multi-parameter classes of methods of any presribed order is presented. In particular, two classes of cubically and fourth order convergent iterative methods for simple zeros of polynomial equations are derived. As special cases, the cubically convergent class includes the one-parameter Hansen-Patricks family and other well-known Laguerre's, Halley's and Ostrowski's methods. Additionally, methods of any order which are based on Taylor expansion of certain rational functions are developed. Modified methods for extracting multiple zeros are briefly discussed.

Original language	English (US)
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	6573-6578
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1583217
State	Published - Dec 1 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: Dec 12 2005 → Dec 15 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Other

Other	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 12/15/05

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10.1109/CDC.2005.1583217

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Hasan, M. A. (2005). A class of higher order algorithms for computing polynomial zeros. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 6573-6578). Article 1583217 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583217

A class of higher order algorithms for computing polynomial zeros. / Hasan, Mohammed A.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6573-6578 1583217 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hasan, MA 2005, A class of higher order algorithms for computing polynomial zeros. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583217, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 6573-6578, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583217

Hasan MA. A class of higher order algorithms for computing polynomial zeros. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6573-6578. 1583217. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583217

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A class of higher order algorithms for computing polynomial zeros

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