Algorithmic aspects of sums of hermitian squares

Burgdorf, Sabine; Cafuta, Kristijan; Klep, Igor; Povh, Janez

Algorithmic aspects of sums of hermitian squares

Dateien

Burgdorf.pdfGröße: 437.55 KBDownloads: 120

Datum

2012

Autor:innen

Burgdorf, Sabine

Cafuta, Kristijan

Klep, Igor

Povh, Janez

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

sum of squares, semidefinite programming, noncommutative polynomial, Matlab Toolbox, Newton polytope, free positivity

Zitieren

ISO 690

BURGDORF, 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>

Universitätsbibliographie

Nein