Algorithmic aspects of sums of hermitian squares

Loading...
Thumbnail Image
Date
2012
Authors
Cafuta, Kristijan
Povh, Janez
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
Konstanzer Schriften in Mathematik; 293
URI (citable link)
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Working Paper/Technical Report
Publication status
Published in
Abstract
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.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
sum of squares,semidefinite programming,noncommutative polynomial,Matlab Toolbox,Newton polytope,free positivity
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
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>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
No
Refereed