Real root-finding

Authors:
Victor Y. Pan;Brian Murphy;Rhys Eric Rosholt;Guoliang Qian;Yuqing Tang
Affiliations:
Lehman College, The City University of New York, Bronx, NY;Lehman College, The City University of New York, Bronx, NY;Lehman College, The City University of New York, Bronx, NY;The City University of New York, New York, NY;The City University of New York, New York, NY
Venue:
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Year:
2007

Citing 27
Cited 6

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Abstract

In this paper we seek all real roots of a polynomial with real coefficients and real and nonreal roots. Somewhat paradoxically, one of the most effective solutions is by approximating these real roots semi-numerically together with all nonreal roots. Alternative methods are symbolic, based on Descartes' rule of signs (which can be combined with the continued fraction approximation algorithm) or the Sturm (or Sturm-Habicht) sequences. We combine various old and new techniques to devise semi-numerical algorithms that are effective where the real roots do not lie near the nonreal ones.