A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems
Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual v...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Tagungsbericht |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 148 |
|---|---|
| container_issue | |
| container_start_page | 143 |
| container_title | |
| container_volume | |
| creator | Bucker, H.M. |
| description | Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed. The algorithm is inspired by a recent transpose-free 1-norm quasi-minimal residual method (TFQMR/sub 1/) in that it applies the 1-norm quasi-minimal residual approach to Bi-CGSTAB in the same way as TFQMR/sub 1/ is derived from the conjugate gradient squared method (CGS). There is also an intimate connection to a method called QMRCGSTAB that is based on applying the (Euclidean norm) quasi-minimal residual approach to Bi-CGSTAB. Numerical examples are used to compare the convergence behavior of Bi-CGSTAB and its 1-norm quasi-minimal residual variant. |
| doi_str_mv | 10.1109/ICPPW.2001.951918 |
| format | Conference Proceeding |
| fullrecord | <record><control><sourceid>ieee_6IE</sourceid><recordid>TN_cdi_ieee_primary_951918</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>951918</ieee_id><sourcerecordid>951918</sourcerecordid><originalsourceid>FETCH-LOGICAL-i174t-c6afb63a98dae42b9a31436560c40f416b8d84258f43e74168ef1804865d69663</originalsourceid><addsrcrecordid>eNotUFtLwzAYDV7AOfcD9Cl_IPPLtcnjVtwcDBw40beRromLNK0mnbB_b2E-nRscOAehewpTSsE8rsrN5n3KAOjUSGqovkAjxgtJJIePSzQxhYZCDRFTAFdoRAefMKDqBt3m_AXAgEs5QtUMU9J2KeKfo82BxNCGaBucXA71cSC_NgXb9rjzuD84PA-kXL5uZ3Nsm88uhf4Qse8Sbrs2n2J0fQp73ITW2YTzKfcu5jt07W2T3eQfx-ht8bQtn8n6ZbkqZ2sSaCF6slfWV4pbo2vrBKuM5VRwJRXsBXhBVaVrLZjUXnBXDFo7TzUIrWStjFJ8jB7OvcE5t_tOw4502p3f4X-j6lZl</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype></control><display><type>conference_proceeding</type><title>A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems</title><source>IEEE Electronic Library (IEL) Conference Proceedings</source><creator>Bucker, H.M.</creator><creatorcontrib>Bucker, H.M.</creatorcontrib><description>Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed. The algorithm is inspired by a recent transpose-free 1-norm quasi-minimal residual method (TFQMR/sub 1/) in that it applies the 1-norm quasi-minimal residual approach to Bi-CGSTAB in the same way as TFQMR/sub 1/ is derived from the conjugate gradient squared method (CGS). There is also an intimate connection to a method called QMRCGSTAB that is based on applying the (Euclidean norm) quasi-minimal residual approach to Bi-CGSTAB. Numerical examples are used to compare the convergence behavior of Bi-CGSTAB and its 1-norm quasi-minimal residual variant.</description><identifier>ISSN: 1530-2016</identifier><identifier>ISBN: 9780769512600</identifier><identifier>ISBN: 0769512607</identifier><identifier>EISSN: 2375-530X</identifier><identifier>DOI: 10.1109/ICPPW.2001.951918</identifier><language>eng</language><publisher>IEEE</publisher><subject>Character generation ; Convergence of numerical methods ; Equations ; Gradient methods ; Hardware ; Iterative algorithms ; Iterative methods ; Large-scale systems ; Linear systems ; Parallel processing</subject><ispartof>Proceedings International Conference on Parallel Processing Workshops, 2001, p.143-148</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/951918$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,777,781,786,787,2052,4036,4037,27906,54901</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/951918$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Bucker, H.M.</creatorcontrib><title>A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems</title><title>Proceedings International Conference on Parallel Processing Workshops</title><addtitle>ICPPW</addtitle><description>Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed. The algorithm is inspired by a recent transpose-free 1-norm quasi-minimal residual method (TFQMR/sub 1/) in that it applies the 1-norm quasi-minimal residual approach to Bi-CGSTAB in the same way as TFQMR/sub 1/ is derived from the conjugate gradient squared method (CGS). There is also an intimate connection to a method called QMRCGSTAB that is based on applying the (Euclidean norm) quasi-minimal residual approach to Bi-CGSTAB. Numerical examples are used to compare the convergence behavior of Bi-CGSTAB and its 1-norm quasi-minimal residual variant.</description><subject>Character generation</subject><subject>Convergence of numerical methods</subject><subject>Equations</subject><subject>Gradient methods</subject><subject>Hardware</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>Large-scale systems</subject><subject>Linear systems</subject><subject>Parallel processing</subject><issn>1530-2016</issn><issn>2375-530X</issn><isbn>9780769512600</isbn><isbn>0769512607</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2001</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNotUFtLwzAYDV7AOfcD9Cl_IPPLtcnjVtwcDBw40beRromLNK0mnbB_b2E-nRscOAehewpTSsE8rsrN5n3KAOjUSGqovkAjxgtJJIePSzQxhYZCDRFTAFdoRAefMKDqBt3m_AXAgEs5QtUMU9J2KeKfo82BxNCGaBucXA71cSC_NgXb9rjzuD84PA-kXL5uZ3Nsm88uhf4Qse8Sbrs2n2J0fQp73ITW2YTzKfcu5jt07W2T3eQfx-ht8bQtn8n6ZbkqZ2sSaCF6slfWV4pbo2vrBKuM5VRwJRXsBXhBVaVrLZjUXnBXDFo7TzUIrWStjFJ8jB7OvcE5t_tOw4502p3f4X-j6lZl</recordid><startdate>2001</startdate><enddate>2001</enddate><creator>Bucker, H.M.</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>2001</creationdate><title>A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems</title><author>Bucker, H.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i174t-c6afb63a98dae42b9a31436560c40f416b8d84258f43e74168ef1804865d69663</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Character generation</topic><topic>Convergence of numerical methods</topic><topic>Equations</topic><topic>Gradient methods</topic><topic>Hardware</topic><topic>Iterative algorithms</topic><topic>Iterative methods</topic><topic>Large-scale systems</topic><topic>Linear systems</topic><topic>Parallel processing</topic><toplevel>online_resources</toplevel><creatorcontrib>Bucker, H.M.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bucker, H.M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems</atitle><btitle>Proceedings International Conference on Parallel Processing Workshops</btitle><stitle>ICPPW</stitle><date>2001</date><risdate>2001</risdate><spage>143</spage><epage>148</epage><pages>143-148</pages><issn>1530-2016</issn><eissn>2375-530X</eissn><isbn>9780769512600</isbn><isbn>0769512607</isbn><abstract>Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed. The algorithm is inspired by a recent transpose-free 1-norm quasi-minimal residual method (TFQMR/sub 1/) in that it applies the 1-norm quasi-minimal residual approach to Bi-CGSTAB in the same way as TFQMR/sub 1/ is derived from the conjugate gradient squared method (CGS). There is also an intimate connection to a method called QMRCGSTAB that is based on applying the (Euclidean norm) quasi-minimal residual approach to Bi-CGSTAB. Numerical examples are used to compare the convergence behavior of Bi-CGSTAB and its 1-norm quasi-minimal residual variant.</abstract><pub>IEEE</pub><doi>10.1109/ICPPW.2001.951918</doi><tpages>6</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 1530-2016 |
| ispartof | Proceedings International Conference on Parallel Processing Workshops, 2001, p.143-148 |
| issn | 1530-2016 2375-530X |
| language | eng |
| recordid | cdi_ieee_primary_951918 |
| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Character generation Convergence of numerical methods Equations Gradient methods Hardware Iterative algorithms Iterative methods Large-scale systems Linear systems Parallel processing |
| title | A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T18%3A35%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ieee_6IE&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=A%201-norm%20quasi-minimal%20residual%20variant%20of%20the%20Bi-CGSTAB%20algorithm%20for%20nonsymmetric%20linear%20systems&rft.btitle=Proceedings%20International%20Conference%20on%20Parallel%20Processing%20Workshops&rft.au=Bucker,%20H.M.&rft.date=2001&rft.spage=143&rft.epage=148&rft.pages=143-148&rft.issn=1530-2016&rft.eissn=2375-530X&rft.isbn=9780769512600&rft.isbn_list=0769512607&rft_id=info:doi/10.1109/ICPPW.2001.951918&rft_dat=%3Cieee_6IE%3E951918%3C/ieee_6IE%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_ieee_id=951918&rfr_iscdi=true |