Verified error bounds for real solutions of positive-dimensional polynomial systems

Zhengfeng Yang, Lihong Zhi, Yijun Zhu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Scopus citations

Abstract

In this paper, we propose two algorithms for verifying the existence of real solutions of positive-dimensional polynomial systems. The first one is based on the critical point method and the homotopy continuation method. It targets for verifying the existence of real roots on each connected component of an algebraic variety V ∩ Rn defined by polynomial equations. The second one is based on the low-rank moment matrix completion method and aims for verifying the existence of at least one real roots on V ∩Rn. Combined both algorithms with the verification algorithms for zerodimensional polynomial systems, we are able to find verified real solutions of positive-dimensional polynomial systems very efficiently for a large set of examples.

Original languageEnglish
Title of host publicationISSAC 2013 - Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation
Pages371-378
Number of pages8
DOIs
StatePublished - 2013
Event38th International Symposium on Symbolic and Algebraic Computation, ISSAC 2013 - Boston, MA, United States
Duration: 26 Jun 201329 Jun 2013

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference38th International Symposium on Symbolic and Algebraic Computation, ISSAC 2013
Country/TerritoryUnited States
CityBoston, MA
Period26/06/1329/06/13

Keywords

  • Error bounds
  • Positive-dimensional polynomial systems
  • Real solutions
  • Verification

Fingerprint

Dive into the research topics of 'Verified error bounds for real solutions of positive-dimensional polynomial systems'. Together they form a unique fingerprint.

Cite this