Incremental condition estimation for sparse matrices
Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estim...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on matrix analysis and applications 1990-10, Vol.11 (4), p.644-659 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 659 |
|---|---|
| container_issue | 4 |
| container_start_page | 644 |
| container_title | SIAM journal on matrix analysis and applications |
| container_volume | 11 |
| creator | BISCHOF, C. H LEWIS, J. G PIERCE, D. J |
| description | Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estimator for dense matrices was originally suggested by Bischof. In this paper this scheme is generalized to handle sparse triangular matrices, especially those that are factors of sparse matrices. Numerical experiments on a variety of matrices demonstrate the reliability of this scheme in estimating the smallest singular value. A partial description of its implementation in a sparse matrix factorization code further illustrates its practicality. |
| doi_str_mv | 10.1137/0611047 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_7206513</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2596844151</sourcerecordid><originalsourceid>FETCH-LOGICAL-c238t-d8d9c551ff8a6e890eddb64a496efb07eaba3832fbbfbe20c4a67f61048b4f8c3</originalsourceid><addsrcrecordid>eNpFkE1LAzEQhoMoWKv4FxYRPK3OJNl8HKX4USh40XPIZhPc0iY12R7890YtepqX4WF43iHkEuEWkck7EIjA5RGZIeiulSjoMZmBqplLrU7JWSlrABRc44zwZXTZb32c7KZxKQ7jNKbY-DKNW_sTQ8pN2dlcfFM3eXS-nJOTYDfFXxzmnLw9PrwuntvVy9Nycb9qHWVqagc1aNd1GIKywisNfhh6wS3XwocepLe9ZYrR0Peh9xQct0IGUe1Vz4NybE6ufu-mqmOKGyfv3qtk9G4ykoLokP1Du5w-9lXcrNM-x-plNGW1MUVRoZtfyOVUSvbB7HItmD8Ngvl-mzm8rZLXh3O2OLsJ2UY3lj-8AwlCIfsCj-BrNA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>923798216</pqid></control><display><type>article</type><title>Incremental condition estimation for sparse matrices</title><source>SIAM Journals Online</source><creator>BISCHOF, C. H ; LEWIS, J. G ; PIERCE, D. J</creator><creatorcontrib>BISCHOF, C. H ; LEWIS, J. G ; PIERCE, D. J</creatorcontrib><description>Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estimator for dense matrices was originally suggested by Bischof. In this paper this scheme is generalized to handle sparse triangular matrices, especially those that are factors of sparse matrices. Numerical experiments on a variety of matrices demonstrate the reliability of this scheme in estimating the smallest singular value. A partial description of its implementation in a sparse matrix factorization code further illustrates its practicality.</description><identifier>ISSN: 0895-4798</identifier><identifier>EISSN: 1095-7162</identifier><identifier>DOI: 10.1137/0611047</identifier><identifier>CODEN: SJMAEL</identifier><language>eng</language><publisher>Philadelphia, PA: Society for Industrial and Applied Mathematics</publisher><subject>990200 - Mathematics & Computers ; ALGORITHMS ; Eigenvalues ; Eigenvectors ; Estimates ; Exact sciences and technology ; Linear algebra ; MATHEMATICAL LOGIC ; Mathematics ; MATHEMATICS AND COMPUTING ; MATRICES ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical linear algebra ; NUMERICAL SOLUTION ; OPTIMIZATION ; PARALLEL PROCESSING ; PROGRAMMING ; Sciences and techniques of general use ; Sparsity</subject><ispartof>SIAM journal on matrix analysis and applications, 1990-10, Vol.11 (4), p.644-659</ispartof><rights>1992 INIST-CNRS</rights><rights>[Copyright] © 1990 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c238t-d8d9c551ff8a6e890eddb64a496efb07eaba3832fbbfbe20c4a67f61048b4f8c3</citedby><cites>FETCH-LOGICAL-c238t-d8d9c551ff8a6e890eddb64a496efb07eaba3832fbbfbe20c4a67f61048b4f8c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,309,310,314,776,780,785,786,881,3171,23909,23910,25118,27901,27902</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5070681$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/7206513$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>BISCHOF, C. H</creatorcontrib><creatorcontrib>LEWIS, J. G</creatorcontrib><creatorcontrib>PIERCE, D. J</creatorcontrib><title>Incremental condition estimation for sparse matrices</title><title>SIAM journal on matrix analysis and applications</title><description>Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estimator for dense matrices was originally suggested by Bischof. In this paper this scheme is generalized to handle sparse triangular matrices, especially those that are factors of sparse matrices. Numerical experiments on a variety of matrices demonstrate the reliability of this scheme in estimating the smallest singular value. A partial description of its implementation in a sparse matrix factorization code further illustrates its practicality.</description><subject>990200 - Mathematics & Computers</subject><subject>ALGORITHMS</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Estimates</subject><subject>Exact sciences and technology</subject><subject>Linear algebra</subject><subject>MATHEMATICAL LOGIC</subject><subject>Mathematics</subject><subject>MATHEMATICS AND COMPUTING</subject><subject>MATRICES</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical linear algebra</subject><subject>NUMERICAL SOLUTION</subject><subject>OPTIMIZATION</subject><subject>PARALLEL PROCESSING</subject><subject>PROGRAMMING</subject><subject>Sciences and techniques of general use</subject><subject>Sparsity</subject><issn>0895-4798</issn><issn>1095-7162</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1990</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpFkE1LAzEQhoMoWKv4FxYRPK3OJNl8HKX4USh40XPIZhPc0iY12R7890YtepqX4WF43iHkEuEWkck7EIjA5RGZIeiulSjoMZmBqplLrU7JWSlrABRc44zwZXTZb32c7KZxKQ7jNKbY-DKNW_sTQ8pN2dlcfFM3eXS-nJOTYDfFXxzmnLw9PrwuntvVy9Nycb9qHWVqagc1aNd1GIKywisNfhh6wS3XwocepLe9ZYrR0Peh9xQct0IGUe1Vz4NybE6ufu-mqmOKGyfv3qtk9G4ykoLokP1Du5w-9lXcrNM-x-plNGW1MUVRoZtfyOVUSvbB7HItmD8Ngvl-mzm8rZLXh3O2OLsJ2UY3lj-8AwlCIfsCj-BrNA</recordid><startdate>19901001</startdate><enddate>19901001</enddate><creator>BISCHOF, C. H</creator><creator>LEWIS, J. G</creator><creator>PIERCE, D. J</creator><general>Society for Industrial and Applied Mathematics</general><general>SIAM</general><scope>IQODW</scope><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><scope>OTOTI</scope></search><sort><creationdate>19901001</creationdate><title>Incremental condition estimation for sparse matrices</title><author>BISCHOF, C. H ; LEWIS, J. G ; PIERCE, D. J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c238t-d8d9c551ff8a6e890eddb64a496efb07eaba3832fbbfbe20c4a67f61048b4f8c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1990</creationdate><topic>990200 - Mathematics & Computers</topic><topic>ALGORITHMS</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Estimates</topic><topic>Exact sciences and technology</topic><topic>Linear algebra</topic><topic>MATHEMATICAL LOGIC</topic><topic>Mathematics</topic><topic>MATHEMATICS AND COMPUTING</topic><topic>MATRICES</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical linear algebra</topic><topic>NUMERICAL SOLUTION</topic><topic>OPTIMIZATION</topic><topic>PARALLEL PROCESSING</topic><topic>PROGRAMMING</topic><topic>Sciences and techniques of general use</topic><topic>Sparsity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BISCHOF, C. H</creatorcontrib><creatorcontrib>LEWIS, J. G</creatorcontrib><creatorcontrib>PIERCE, D. J</creatorcontrib><collection>Pascal-Francis</collection><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 & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & 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 (ProQuest)</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 & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>One Business (ProQuest)</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><collection>OSTI.GOV</collection><jtitle>SIAM journal on matrix analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BISCHOF, C. H</au><au>LEWIS, J. G</au><au>PIERCE, D. J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Incremental condition estimation for sparse matrices</atitle><jtitle>SIAM journal on matrix analysis and applications</jtitle><date>1990-10-01</date><risdate>1990</risdate><volume>11</volume><issue>4</issue><spage>644</spage><epage>659</epage><pages>644-659</pages><issn>0895-4798</issn><eissn>1095-7162</eissn><coden>SJMAEL</coden><abstract>Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estimator for dense matrices was originally suggested by Bischof. In this paper this scheme is generalized to handle sparse triangular matrices, especially those that are factors of sparse matrices. Numerical experiments on a variety of matrices demonstrate the reliability of this scheme in estimating the smallest singular value. A partial description of its implementation in a sparse matrix factorization code further illustrates its practicality.</abstract><cop>Philadelphia, PA</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/0611047</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0895-4798 |
| ispartof | SIAM journal on matrix analysis and applications, 1990-10, Vol.11 (4), p.644-659 |
| issn | 0895-4798 1095-7162 |
| language | eng |
| recordid | cdi_osti_scitechconnect_7206513 |
| source | SIAM Journals Online |
| subjects | 990200 - Mathematics & Computers ALGORITHMS Eigenvalues Eigenvectors Estimates Exact sciences and technology Linear algebra MATHEMATICAL LOGIC Mathematics MATHEMATICS AND COMPUTING MATRICES Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra NUMERICAL SOLUTION OPTIMIZATION PARALLEL PROCESSING PROGRAMMING Sciences and techniques of general use Sparsity |
| title | Incremental condition estimation for sparse matrices |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-07T13%3A36%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Incremental%20condition%20estimation%20for%20sparse%20matrices&rft.jtitle=SIAM%20journal%20on%20matrix%20analysis%20and%20applications&rft.au=BISCHOF,%20C.%20H&rft.date=1990-10-01&rft.volume=11&rft.issue=4&rft.spage=644&rft.epage=659&rft.pages=644-659&rft.issn=0895-4798&rft.eissn=1095-7162&rft.coden=SJMAEL&rft_id=info:doi/10.1137/0611047&rft_dat=%3Cproquest_osti_%3E2596844151%3C/proquest_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=923798216&rft_id=info:pmid/&rfr_iscdi=true |