Total nonnegativity of finite Hurwitz matrices and root location of polynomials
Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
| Type of Publication: | Working Paper/Technical Report |
| Publication status: | Published |
| URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-2--t62blplni8h73 |
| Author: | Adm, Mohammad; Garloff, Jürgen; Tyaglov, Mikhail |
| Year of publication: | 2017 |
| Series: | Konstanzer Schriften in Mathematik ; 368 |
| Summary: |
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
|
| MSC Classification: | 15B48, 26C10, 15A18, 15B05 |
| Subject (DDC): | 510 Mathematics |
| Keywords: | Hurwitz matrix, totally nonnegative matrix, stable polynomial, quasi-stable polynomial, R-function |
| Link to License: | In Copyright |
| Bibliography of Konstanz: | Yes |
Cite This
Files in this item
![[PDF]](/themes/Kops/images/mimes/pdf.png "PDF file"){kind=small}
ADM, Mohammad, Jürgen GARLOFF, Mikhail TYAGLOV, 2017. Total nonnegativity of finite Hurwitz matrices and root location of polynomials
@techreport{Adm2017-11-09T23:17:28ZTotal-40767, series={Konstanzer Schriften in Mathematik}, title={Total nonnegativity of finite Hurwitz matrices and root location of polynomials}, year={2017}, number={368}, author={Adm, Mohammad and Garloff, Jürgen and Tyaglov, Mikhail} }
<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/rdf/resource/123456789/40767"> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dc:creator>Tyaglov, Mikhail</dc:creator> <dc:language>eng</dc:language> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/40767/3/Adm_2--t62blplni8h73.pdf"/> <dc:creator>Garloff, Jürgen</dc:creator> <dcterms:title>Total nonnegativity of finite Hurwitz matrices and root location of polynomials</dcterms:title> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/40767/3/Adm_2--t62blplni8h73.pdf"/> <dc:contributor>Adm, Mohammad</dc:contributor> <dc:contributor>Garloff, Jürgen</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Tyaglov, Mikhail</dc:contributor> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-11-28T16:37:24Z</dcterms:available> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/52"/> <dc:rights>terms-of-use</dc:rights> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-11-28T16:37:24Z</dc:date> <dcterms:issued>2017-11-09T23:17:28Z</dcterms:issued> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/40767"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dcterms:abstract xml:lang="eng">In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.</dcterms:abstract> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/52"/> <dc:creator>Adm, Mohammad</dc:creator> </rdf:Description> </rdf:RDF>
Downloads since Nov 28, 2017 (Information about access statistics)
| Adm_2--t62blplni8h73.pdf | 388 |
This item appears in the following Collection(s)
Search KOPS
Browse
My Account
