Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
An SDP-based method for the real radical ideal membership test
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2017 (English)In: Proceedings of the 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 86-93Conference paper, Published paper (Refereed)
Abstract [en]

Let V be the set of real solutions of a system of multivariate polynomial equations with real coefficients. The real radical ideal (RRI) of V is the infinite set of multivariate polynomials that vanish on V. We give theoretical results that yield a finite step numerical algorithm for testing if a given polynomial is a member of this RRI. The paper exploits recent work that connects solution sets of such real polynomial systems with solution sets of semidefinite programming, SDP, problems involving moment matrices. We take advantage of an SDP technique called facial reduction. This technique regularizes our problem by projecting the feasible set onto the so-called minimal face. In addition, we use the Douglas-Rachford iterative approach which has advantages over traditional interior point methods for our application. If V has finitely many real solutions, then our method yields a finite set of polynomials in the form of a geometric involutive basis that are generators of the RRI and form an RRI membership test. In the case where the set V has real solution components of positive dimension, and given an input polynomial of degree d, our method can also decide RRI membership via a truncated geometric involutive basis of degree d. Examples are given to illustrate our approach and its advantages that remove multiplicities and sums of squares that cause illconditioning for real solutions of polynomial systems.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017. p. 86-93
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-248408DOI: 10.1109/SYNASC.2017.00025Scopus ID: 2-s2.0-85058313722ISBN: 9781538626269 (print)OAI: oai:DiVA.org:kth-248408DiVA, id: diva2:1302910
Conference
19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2017; Timisoara; Romania; 21 September 2017 through 24 September 2017
Note

QC 20190529

Available from: 2019-04-07 Created: 2019-04-07 Last updated: 2019-08-22Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Wang, Fei
By organisation
Optimization and Systems Theory
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 6 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf