Exact Solutions in Structured Low-Rank Approximation
Identifieur interne : 000D41 ( Hal/Checkpoint ); précédent : 000D40; suivant : 000D42Exact Solutions in Structured Low-Rank Approximation
Auteurs : Giorgio Ottaviani [Italie] ; Pierre-Jean Spaenlehauer [France] ; Bernd Sturmfels [États-Unis]Source :
- SIAM Journal on Matrix Analysis and Applications [ 0895-4798 ] ; 2014.
Abstract
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.
Url:
Links toward previous steps (curation, corpus...)
Links to Exploration step
Hal:hal-00953702Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Exact Solutions in Structured Low-Rank Approximation</title>
<author><name sortKey="Ottaviani, Giorgio" sort="Ottaviani, Giorgio" uniqKey="Ottaviani G" first="Giorgio" last="Ottaviani">Giorgio Ottaviani</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-136433" status="VALID"><orgName>Dipartimento di Matematica "Ulisse Dini"</orgName>
<desc><address><addrLine>Viale Morgagni, 67/a - 50134 Firenze</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.math.unifi.it/dipartimento</ref>
</desc>
<listRelation><relation active="#struct-148408" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-148408" type="direct"><org type="institution" xml:id="struct-148408" status="VALID"><orgName>Università degli Studi di Firenze [Firenze]</orgName>
<desc><address><addrLine>P.zza S.Marco, 4 - 50121 Firenze</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.unifi.it/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Italie</country>
</affiliation>
</author>
<author><name sortKey="Spaenlehauer, Pierre Jean" sort="Spaenlehauer, Pierre Jean" uniqKey="Spaenlehauer P" first="Pierre-Jean" last="Spaenlehauer">Pierre-Jean Spaenlehauer</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-119560" status="VALID"><idno type="RNSR">201020971F</idno>
<orgName>Cryptology, Arithmetic: Hardware and Software</orgName>
<orgName type="acronym">CARAMEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/caramel</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Sturmfels, Bernd" sort="Sturmfels, Bernd" uniqKey="Sturmfels B" first="Bernd" last="Sturmfels">Bernd Sturmfels</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-29123" status="VALID"><orgName>Department of Mathematics</orgName>
<desc><address><country key="US"></country>
</address>
<ref type="url">http://math.berkeley.edu/</ref>
</desc>
<listRelation><relation active="#struct-300674" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300674" type="direct"><org type="institution" xml:id="struct-300674" status="VALID"><orgName>University of California [Berkeley]</orgName>
<desc><address><addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-00953702</idno>
<idno type="halId">hal-00953702</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-00953702</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-00953702</idno>
<date when="2014">2014</date>
<idno type="wicri:Area/Hal/Corpus">002081</idno>
<idno type="wicri:Area/Hal/Curation">002081</idno>
<idno type="wicri:Area/Hal/Checkpoint">000D41</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000D41</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Exact Solutions in Structured Low-Rank Approximation</title>
<author><name sortKey="Ottaviani, Giorgio" sort="Ottaviani, Giorgio" uniqKey="Ottaviani G" first="Giorgio" last="Ottaviani">Giorgio Ottaviani</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-136433" status="VALID"><orgName>Dipartimento di Matematica "Ulisse Dini"</orgName>
<desc><address><addrLine>Viale Morgagni, 67/a - 50134 Firenze</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.math.unifi.it/dipartimento</ref>
</desc>
<listRelation><relation active="#struct-148408" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-148408" type="direct"><org type="institution" xml:id="struct-148408" status="VALID"><orgName>Università degli Studi di Firenze [Firenze]</orgName>
<desc><address><addrLine>P.zza S.Marco, 4 - 50121 Firenze</addrLine>
<country key="IT"></country>
</address>
<ref type="url">http://www.unifi.it/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Italie</country>
</affiliation>
</author>
<author><name sortKey="Spaenlehauer, Pierre Jean" sort="Spaenlehauer, Pierre Jean" uniqKey="Spaenlehauer P" first="Pierre-Jean" last="Spaenlehauer">Pierre-Jean Spaenlehauer</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-119560" status="VALID"><idno type="RNSR">201020971F</idno>
<orgName>Cryptology, Arithmetic: Hardware and Software</orgName>
<orgName type="acronym">CARAMEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/caramel</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Sturmfels, Bernd" sort="Sturmfels, Bernd" uniqKey="Sturmfels B" first="Bernd" last="Sturmfels">Bernd Sturmfels</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-29123" status="VALID"><orgName>Department of Mathematics</orgName>
<desc><address><country key="US"></country>
</address>
<ref type="url">http://math.berkeley.edu/</ref>
</desc>
<listRelation><relation active="#struct-300674" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300674" type="direct"><org type="institution" xml:id="struct-300674" status="VALID"><orgName>University of California [Berkeley]</orgName>
<desc><address><addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</analytic>
<series><title level="j">SIAM Journal on Matrix Analysis and Applications</title>
<idno type="ISSN">0895-4798</idno>
<imprint><date type="datePub">2014</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.</div>
</front>
</TEI>
<hal api="V3"><titleStmt><title xml:lang="en">Exact Solutions in Structured Low-Rank Approximation</title>
<author role="aut"><persName><forename type="first">Giorgio</forename>
<surname>Ottaviani</surname>
</persName>
<email></email>
<idno type="halauthor">991773</idno>
<affiliation ref="#struct-136433"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Pierre-Jean</forename>
<surname>Spaenlehauer</surname>
</persName>
<email></email>
<idno type="idhal">pspaenle</idno>
<idno type="halauthor">991750</idno>
<affiliation ref="#struct-119560"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Bernd</forename>
<surname>Sturmfels</surname>
</persName>
<email></email>
<idno type="halauthor">991774</idno>
<affiliation ref="#struct-29123"></affiliation>
</author>
<editor role="depositor"><persName><forename>Pierre-Jean</forename>
<surname>Spaenlehauer</surname>
</persName>
<email>pierre-jean.spaenlehauer@inria.fr</email>
</editor>
</titleStmt>
<editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2014-02-28 14:54:44</date>
<date type="whenWritten">2013-11-11</date>
<date type="whenModified">2015-12-16 01:10:05</date>
<date type="whenReleased">2014-02-28 14:54:44</date>
<date type="whenProduced">2014</date>
</edition>
<respStmt><resp>contributor</resp>
<name key="167454"><persName><forename>Pierre-Jean</forename>
<surname>Spaenlehauer</surname>
</persName>
<email>pierre-jean.spaenlehauer@inria.fr</email>
</name>
</respStmt>
</editionStmt>
<publicationStmt><distributor>CCSD</distributor>
<idno type="halId">hal-00953702</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-00953702</idno>
<idno type="halBibtex">ottaviani:hal-00953702</idno>
<idno type="halRefHtml">SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2014, 35, 4, pp.1521-1542</idno>
<idno type="halRef">SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2014, 35, 4, pp.1521-1542</idno>
</publicationStmt>
<seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
<idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
<idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
<idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno>
<idno type="stamp" n="LORIA2">Publications du LORIA</idno>
<idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno>
<idno type="stamp" n="LORIA-ACGI" p="LORIA">Algorithmique, calcul, image et géométrie</idno>
<idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
<idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
<idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
<idno type="stamp" n="LORIA-ALGO-TEST5">LORIA-ALGO-TEST5 </idno>
<idno type="stamp" n="INRIA2">INRIA 2</idno>
</seriesStmt>
<notesStmt><note type="audience" n="2">International</note>
<note type="popular" n="0">No</note>
<note type="peer" n="1">Yes</note>
</notesStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Exact Solutions in Structured Low-Rank Approximation</title>
<author role="aut"><persName><forename type="first">Giorgio</forename>
<surname>Ottaviani</surname>
</persName>
<idno type="halAuthorId">991773</idno>
<affiliation ref="#struct-136433"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Pierre-Jean</forename>
<surname>Spaenlehauer</surname>
</persName>
<idno type="idHal">pspaenle</idno>
<idno type="halAuthorId">991750</idno>
<affiliation ref="#struct-119560"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Bernd</forename>
<surname>Sturmfels</surname>
</persName>
<idno type="halAuthorId">991774</idno>
<affiliation ref="#struct-29123"></affiliation>
</author>
</analytic>
<monogr><idno type="halJournalId" status="VALID">18943</idno>
<idno type="issn">0895-4798</idno>
<title level="j">SIAM Journal on Matrix Analysis and Applications</title>
<imprint><publisher>Society for Industrial and Applied Mathematics</publisher>
<biblScope unit="serie">35</biblScope>
<biblScope unit="volume">4</biblScope>
<biblScope unit="pp">1521-1542</biblScope>
<date type="datePub">2014</date>
</imprint>
</monogr>
<idno type="arxiv">1311.2376</idno>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><classCode scheme="halDomain" n="info.info-sc">Computer Science [cs]/Symbolic Computation [cs.SC]</classCode>
<classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
<classCode scheme="halDomain" n="math.math-ag">Mathematics [math]/Algebraic Geometry [math.AG]</classCode>
<classCode scheme="halDomain" n="stat.co">Statistics [stat]/Computation [stat.CO]</classCode>
<classCode scheme="halTypology" n="ART">Journal articles</classCode>
</textClass>
<abstract xml:lang="en">Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.</abstract>
</profileDesc>
</hal>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000D41 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Checkpoint/biblio.hfd -nk 000D41 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Hal |étape= Checkpoint |type= RBID |clé= Hal:hal-00953702 |texte= Exact Solutions in Structured Low-Rank Approximation }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |