License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.5
URN: urn:nbn:de:0030-drops-81965
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8196/
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Raghavendra, Prasad ; Ryder, Nick ; Srivastava, Nikhil

Real Stability Testing

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LIPIcs-ITCS-2017-5.pdf (0.5 MB)

Abstract

We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials preserves real-rootedness. The proof exploits properties of hyperbolic polynomials to reduce real stability testing to testing nonnegativity of a finite number of polynomials on an interval.

BibTeX - Entry

@InProceedings{raghavendra_et_al:LIPIcs:2017:8196,
  author =	{Prasad Raghavendra and Nick Ryder and Nikhil Srivastava},
  title =	{{Real Stability Testing}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8196},
  URN =		{urn:nbn:de:0030-drops-81965},
  doi =		{10.4230/LIPIcs.ITCS.2017.5},
  annote =	{Keywords: real stable polynomials, hyperbolic polynomials, real rootedness, moment matrix, sturm sequence}
}

Keywords: real stable polynomials, hyperbolic polynomials, real rootedness, moment matrix, sturm sequence
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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