Inertias of Block Band Matrix Completions

Inertias of Block Band Matrix Completions

This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^*&C&D\cr ?&D^*&E}. The full set of completion inertias is described in terms...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on matrix analysis and applications 1998-07, Vol.19 (3), p.583-612
Hauptverfasser: Cohen, Nir, Dancis, Jerome
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 612
container_issue 3
container_start_page 583
container_title SIAM journal on matrix analysis and applications
container_volume 19
creator Cohen, Nir
Dancis, Jerome
description This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^*&C&D\cr ?&D^*&E}. The full set of completion inertias is described in terms of seven linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed. We study the completion inertias of partially specified hermitian block band matrices, using a block generalization of the Dym--Gohberg algorithm. At each inductive step, we use our classification of the possible inertias for hermitian completions of bordered matrices. We show that when all the maximal specified submatrices are invertible, any inertia consistent with Poincare's inequalities is obtainable. These results generalize the nonblock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 813--829]. All our results remain valid for real symmetric completions.
doi_str_mv 10.1137/S0895479895296471
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_923748913</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2596590651</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-1cdcb521bfef640dd6e40fb30a44985369cad9afb9183a76df8bbcee1c3270ec3</originalsourceid><addsrcrecordid>eNplUDtPwzAYtBBIhMIPYIvYGEL9xY4djzSiUKkVAzBbfkopaRzsVIJ_T6KysdwN95IOoVvADwCEL99wLSrKxYSlYJTDGcoAi6rgwMpzlM1yMeuX6CqlPcbAqIAM3W96F8dWpTz4fNUF85mvVG_znRpj-5034TB0bmxDn67RhVddcjd_vEAf66f35qXYvj5vmsdtYUqOxwKMNboqQXvnGcXWMkex1wQrSkVdESaMskJ5LaAmijPra62Nc2DIlHeGLNDdqXeI4evo0ij34Rj7aVKKknBaCyCTCU4mE0NK0Xk5xPag4o8ELOdD5L9DyC_Z0lJp</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>923748913</pqid></control><display><type>article</type><title>Inertias of Block Band Matrix Completions</title><source>SIAM Journals Online</source><source>Business Source Complete</source><creator>Cohen, Nir ; Dancis, Jerome</creator><creatorcontrib>Cohen, Nir ; Dancis, Jerome</creatorcontrib><description><![CDATA[This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^*&C&D\cr ?&D^*&E}. The full set of completion inertias is described in terms of seven linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed. We study the completion inertias of partially specified hermitian block band matrices, using a block generalization of the Dym--Gohberg algorithm. At each inductive step, we use our classification of the possible inertias for hermitian completions of bordered matrices. We show that when all the maximal specified submatrices are invertible, any inertia consistent with Poincare's inequalities is obtainable. These results generalize the nonblock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 813--829]. All our results remain valid for real symmetric completions.]]></description><identifier>ISSN: 0895-4798</identifier><identifier>EISSN: 1095-7162</identifier><identifier>DOI: 10.1137/S0895479895296471</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><ispartof>SIAM journal on matrix analysis and applications, 1998-07, Vol.19 (3), p.583-612</ispartof><rights>[Copyright] © 1998 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c270t-1cdcb521bfef640dd6e40fb30a44985369cad9afb9183a76df8bbcee1c3270ec3</citedby><cites>FETCH-LOGICAL-c270t-1cdcb521bfef640dd6e40fb30a44985369cad9afb9183a76df8bbcee1c3270ec3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3182,27923,27924</link.rule.ids></links><search><creatorcontrib>Cohen, Nir</creatorcontrib><creatorcontrib>Dancis, Jerome</creatorcontrib><title>Inertias of Block Band Matrix Completions</title><title>SIAM journal on matrix analysis and applications</title><description><![CDATA[This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^*&C&D\cr ?&D^*&E}. The full set of completion inertias is described in terms of seven linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed. We study the completion inertias of partially specified hermitian block band matrices, using a block generalization of the Dym--Gohberg algorithm. At each inductive step, we use our classification of the possible inertias for hermitian completions of bordered matrices. We show that when all the maximal specified submatrices are invertible, any inertia consistent with Poincare's inequalities is obtainable. These results generalize the nonblock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 813--829]. All our results remain valid for real symmetric completions.]]></description><issn>0895-4798</issn><issn>1095-7162</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNplUDtPwzAYtBBIhMIPYIvYGEL9xY4djzSiUKkVAzBbfkopaRzsVIJ_T6KysdwN95IOoVvADwCEL99wLSrKxYSlYJTDGcoAi6rgwMpzlM1yMeuX6CqlPcbAqIAM3W96F8dWpTz4fNUF85mvVG_znRpj-5034TB0bmxDn67RhVddcjd_vEAf66f35qXYvj5vmsdtYUqOxwKMNboqQXvnGcXWMkex1wQrSkVdESaMskJ5LaAmijPra62Nc2DIlHeGLNDdqXeI4evo0ij34Rj7aVKKknBaCyCTCU4mE0NK0Xk5xPag4o8ELOdD5L9DyC_Z0lJp</recordid><startdate>19980701</startdate><enddate>19980701</enddate><creator>Cohen, Nir</creator><creator>Dancis, Jerome</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope></search><sort><creationdate>19980701</creationdate><title>Inertias of Block Band Matrix Completions</title><author>Cohen, Nir ; Dancis, Jerome</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-1cdcb521bfef640dd6e40fb30a44985369cad9afb9183a76df8bbcee1c3270ec3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cohen, Nir</creatorcontrib><creatorcontrib>Dancis, Jerome</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>Agricultural &amp; Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on matrix analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cohen, Nir</au><au>Dancis, Jerome</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inertias of Block Band Matrix Completions</atitle><jtitle>SIAM journal on matrix analysis and applications</jtitle><date>1998-07-01</date><risdate>1998</risdate><volume>19</volume><issue>3</issue><spage>583</spage><epage>612</epage><pages>583-612</pages><issn>0895-4798</issn><eissn>1095-7162</eissn><abstract><![CDATA[This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^*&C&D\cr ?&D^*&E}. The full set of completion inertias is described in terms of seven linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed. We study the completion inertias of partially specified hermitian block band matrices, using a block generalization of the Dym--Gohberg algorithm. At each inductive step, we use our classification of the possible inertias for hermitian completions of bordered matrices. We show that when all the maximal specified submatrices are invertible, any inertia consistent with Poincare's inequalities is obtainable. These results generalize the nonblock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 813--829]. All our results remain valid for real symmetric completions.]]></abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/S0895479895296471</doi><tpages>30</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0895-4798
ispartof SIAM journal on matrix analysis and applications, 1998-07, Vol.19 (3), p.583-612
issn 0895-4798
1095-7162
language eng
recordid cdi_proquest_journals_923748913
source SIAM Journals Online; Business Source Complete
title Inertias of Block Band Matrix Completions
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T12%3A41%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Inertias%20of%20Block%20Band%20Matrix%20Completions&rft.jtitle=SIAM%20journal%20on%20matrix%20analysis%20and%20applications&rft.au=Cohen,%20Nir&rft.date=1998-07-01&rft.volume=19&rft.issue=3&rft.spage=583&rft.epage=612&rft.pages=583-612&rft.issn=0895-4798&rft.eissn=1095-7162&rft_id=info:doi/10.1137/S0895479895296471&rft_dat=%3Cproquest_cross%3E2596590651%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=923748913&rft_id=info:pmid/&rfr_iscdi=true