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Real Stability Testing

Authors Prasad Raghavendra, Nick Ryder, Nikhil Srivastava

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Prasad Raghavendra
Nick Ryder
Nikhil Srivastava

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Prasad Raghavendra, Nick Ryder, and Nikhil Srivastava. Real Stability Testing. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ITCS.2017.5

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.

Subject Classification

Keywords
  • real stable polynomials
  • hyperbolic polynomials
  • real rootedness
  • moment matrix
  • sturm sequence

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