2026-07-22T04:52:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8196 2024-03-06T10:39:16Z ddc:004 open_access

Real Stability Testing Raghavendra, Prasad Ryder, Nick Srivastava, Nikhil real stable polynomials hyperbolic polynomials real rootedness moment matrix sturm sequence 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prasad Raghavendra and Nick Ryder and Nikhil Srivastava 2017 Is Part Of LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2017.5 urn:nbn:de:0030-drops-81965 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.5 eng https://creativecommons.org/licenses/by/3.0/legalcode