The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions

Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	SIAM review 2017-12, Vol.59 (4), p.794-800
1. Verfasser:	Shitov, Yaroslav
Format:	Artikel
Sprache:	eng
Schlagworte:	RESEARCH SPOTLIGHTS
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	800
container_issue	4
container_start_page	794
container_title	SIAM review
container_volume	59
creator	Shitov, Yaroslav
description	Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, who discussed this topic in different terms fifteen years before the work of Vavasis. Second, we present a solution of the Cohen-Rothblum problem on rational nonnegative factorizations, which was posed in 1993 and remained open until now.
doi_str_mv	10.1137/16M1080999
format	Article
fullrecord	<record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1137_16M1080999</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>45109253</jstor_id><sourcerecordid>45109253</sourcerecordid><originalsourceid>FETCH-LOGICAL-c253t-a861f1d646d3ace7d2865996d5f1a9f7091aa20af282b762a1df1f52220753713</originalsourceid><addsrcrecordid>eNpFkEFLAzEUhIMoWKsX70LO4up7ySbZeBEp1Qqtitbz8tpNdGu7kWQr9t-7UtHTMPAxzAxjxwjniNJcoJ4gFGCt3WE9BKsyIwB2WQ9A6gzzXO2zg5QW0PlC2h67mr45fh-axr1SW386_kTNOw-eE59QG-uvSz6iWPHHGGZLt0pnfEhpw5_Dct3WoUmHbM_TMrmjX-2zl5vhdDDKxg-3d4PrcTYXSrYZFRo9VjrXlaS5M5UotLJWV8ojWW_AIpEA8qIQM6MFYeXRKyEEGCUNyj473ebOY0gpOl9-xHpFcVMilD_Ty__pHXyyhRepDfGPzFX3SFdHfgMYslLQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions</title><source>Jstor Complete Legacy</source><source>LOCUS - SIAM's Online Journal Archive</source><source>JSTOR Mathematics & Statistics</source><creator>Shitov, Yaroslav</creator><creatorcontrib>Shitov, Yaroslav</creatorcontrib><description>Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, who discussed this topic in different terms fifteen years before the work of Vavasis. Second, we present a solution of the Cohen-Rothblum problem on rational nonnegative factorizations, which was posed in 1993 and remained open until now.</description><identifier>ISSN: 0036-1445</identifier><identifier>EISSN: 1095-7200</identifier><identifier>DOI: 10.1137/16M1080999</identifier><language>eng</language><publisher>Society for Industrial and Applied Mathematics</publisher><subject>RESEARCH SPOTLIGHTS</subject><ispartof>SIAM review, 2017-12, Vol.59 (4), p.794-800</ispartof><rights>Copyright ©2017 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c253t-a861f1d646d3ace7d2865996d5f1a9f7091aa20af282b762a1df1f52220753713</citedby><cites>FETCH-LOGICAL-c253t-a861f1d646d3ace7d2865996d5f1a9f7091aa20af282b762a1df1f52220753713</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/45109253$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/45109253$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,3172,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Shitov, Yaroslav</creatorcontrib><title>The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions</title><title>SIAM review</title><description>Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, who discussed this topic in different terms fifteen years before the work of Vavasis. Second, we present a solution of the Cohen-Rothblum problem on rational nonnegative factorizations, which was posed in 1993 and remained open until now.</description><subject>RESEARCH SPOTLIGHTS</subject><issn>0036-1445</issn><issn>1095-7200</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNpFkEFLAzEUhIMoWKsX70LO4up7ySbZeBEp1Qqtitbz8tpNdGu7kWQr9t-7UtHTMPAxzAxjxwjniNJcoJ4gFGCt3WE9BKsyIwB2WQ9A6gzzXO2zg5QW0PlC2h67mr45fh-axr1SW386_kTNOw-eE59QG-uvSz6iWPHHGGZLt0pnfEhpw5_Dct3WoUmHbM_TMrmjX-2zl5vhdDDKxg-3d4PrcTYXSrYZFRo9VjrXlaS5M5UotLJWV8ojWW_AIpEA8qIQM6MFYeXRKyEEGCUNyj473ebOY0gpOl9-xHpFcVMilD_Ty__pHXyyhRepDfGPzFX3SFdHfgMYslLQ</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>Shitov, Yaroslav</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171201</creationdate><title>The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions</title><author>Shitov, Yaroslav</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c253t-a861f1d646d3ace7d2865996d5f1a9f7091aa20af282b762a1df1f52220753713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>RESEARCH SPOTLIGHTS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shitov, Yaroslav</creatorcontrib><collection>CrossRef</collection><jtitle>SIAM review</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shitov, Yaroslav</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions</atitle><jtitle>SIAM review</jtitle><date>2017-12-01</date><risdate>2017</risdate><volume>59</volume><issue>4</issue><spage>794</spage><epage>800</epage><pages>794-800</pages><issn>0036-1445</issn><eissn>1095-7200</eissn><abstract>Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, who discussed this topic in different terms fifteen years before the work of Vavasis. Second, we present a solution of the Cohen-Rothblum problem on rational nonnegative factorizations, which was posed in 1993 and remained open until now.</abstract><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/16M1080999</doi><tpages>7</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0036-1445
ispartof	SIAM review, 2017-12, Vol.59 (4), p.794-800
issn	0036-1445 1095-7200
language	eng
recordid	cdi_crossref_primary_10_1137_16M1080999
source	Jstor Complete Legacy; LOCUS - SIAM's Online Journal Archive; JSTOR Mathematics & Statistics
subjects	RESEARCH SPOTLIGHTS
title	The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T02%3A20%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Nonnegative%20Rank%20of%20a%20Matrix:%20Hard%20Problems,%20Easy%20Solutions&rft.jtitle=SIAM%20review&rft.au=Shitov,%20Yaroslav&rft.date=2017-12-01&rft.volume=59&rft.issue=4&rft.spage=794&rft.epage=800&rft.pages=794-800&rft.issn=0036-1445&rft.eissn=1095-7200&rft_id=info:doi/10.1137/16M1080999&rft_dat=%3Cjstor_cross%3E45109253%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=45109253&rfr_iscdi=true