Algorithmic aspects of sums of hermitian squares

Lade...
Vorschaubild
Dateien
Burgdorf.pdf
Burgdorf.pdfGröße: 437.55 KBDownloads: 117
Datum
2012
Autor:innen
Cafuta, Kristijan
Povh, Janez
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Auflagebezeichnung
DOI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Open Access Green
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Publikationstyp
Working Paper/Technical Report
Publikationsstatus
Published
Erschienen in
Zusammenfassung

This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and the Newton polytope method, which allows us to use semidefinite programming. For rational polynomials numerical evidence can be tweaked to obtain an exact certificate using rational numbers. In the presence of Slater points, the Peyrl-Parrilo rounding and projecting method applies. On the other hand, in the absence of strict feasibility, a variant of the facial reduction is proposed to reduce the size of the semidefinite program and to enforce the existence of Slater points.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
sum of squares, semidefinite programming, noncommutative polynomial, Matlab Toolbox, Newton polytope, free positivity
Konferenz
Rezension
undefined / . - undefined, undefined
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Datensätze
Zitieren
ISO 690BURGDORF, Sabine, Kristijan CAFUTA, Igor KLEP, Janez POVH, 2012. Algorithmic aspects of sums of hermitian squares
BibTex
@techreport{Burgdorf2012Algor-15338,
  year={2012},
  series={Konstanzer Schriften in Mathematik},
  title={Algorithmic aspects of sums of hermitian squares},
  number={293},
  author={Burgdorf, Sabine and Cafuta, Kristijan and Klep, Igor and Povh, Janez}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/15338">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:abstract xml:lang="eng">This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and the Newton polytope method, which allows us to use semidefinite programming. For rational polynomials numerical evidence can be tweaked to obtain an exact certificate using rational numbers. In the presence of Slater points, the Peyrl-Parrilo rounding and projecting method applies. On the other hand, in the absence of strict feasibility, a variant of the facial reduction is proposed to reduce the size of the semidefinite program and to enforce the existence of Slater points.</dcterms:abstract>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15338/2/Burgdorf.pdf"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:language>eng</dc:language>
    <dc:creator>Cafuta, Kristijan</dc:creator>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/15338"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:contributor>Burgdorf, Sabine</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-01-10T07:58:16Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-01-10T07:58:16Z</dc:date>
    <dc:creator>Burgdorf, Sabine</dc:creator>
    <dc:creator>Klep, Igor</dc:creator>
    <dc:creator>Povh, Janez</dc:creator>
    <dcterms:issued>2012</dcterms:issued>
    <dc:contributor>Cafuta, Kristijan</dc:contributor>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15338/2/Burgdorf.pdf"/>
    <dc:contributor>Povh, Janez</dc:contributor>
    <dcterms:title>Algorithmic aspects of sums of hermitian squares</dcterms:title>
    <dc:contributor>Klep, Igor</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:rights>terms-of-use</dc:rights>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Nein
Begutachtet
Diese Publikation teilen