A class of higher order algorithms for computing polynomial zeros

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages6573-6578
Number of pages6
DOIs
StatePublished - Dec 1 2005
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: Dec 12 2005Dec 15 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
CountrySpain
CitySeville
Period12/12/0512/15/05

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