A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation
Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modifie...
Gespeichert in:
Veröffentlicht in: | Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-7 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 7 |
---|---|
container_issue | 2014 |
container_start_page | 1 |
container_title | Mathematical problems in engineering |
container_volume | 2014 |
creator | Hou, Junxia Lv, Quanyi Xiao, Manyu |
description | Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency. |
doi_str_mv | 10.1155/2014/598716 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1541429281</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1541429281</sourcerecordid><originalsourceid>FETCH-LOGICAL-c346t-ea3148eec5583b0f040e2839f3c15b38a352d7ae36af7d2afab396533714af8c3</originalsourceid><addsrcrecordid>eNqF0ElLxEAQBeAgCq4nz0KDF1GiXb0knaMMbjCDggreYk1SrT3EtHYSl39vDxEPXjxVHT4ej5cku8CPAbQ-ERzUiS5MDtlKsgE6k6kGla_GnwuVgpAP68lm1y04F6DBbCSPp-wGAzYNNewmUOXb2vXOt1Szma-ddfGZ-HYxPGFP7CJg7ajt2Yz6Z18z6wObYngidvvVvFPXU2Az7IP7ZGdvAy6DtpM1i01HOz93K7k_P7ubXKbT64uryek0raTK-pRQgjJEldZGzrnlipMwsrCyAj2XBqUWdY4kM7R5LdDiXBaZljIHhdZUcis5GHNfg38bYpXyxXUVNQ225IeuBK1AiUIYiHT_D134IbSxXVRZxkVhijyqo1FVwXddIFu-BveC4asEXi7XLpdrl-PaUR-O-tm1NX64f_DeiCkSsviLlVFcZvIbsMiH3w</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1566029897</pqid></control><display><type>article</type><title>A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Wiley Online Library (Open Access Collection)</source><source>Alma/SFX Local Collection</source><creator>Hou, Junxia ; Lv, Quanyi ; Xiao, Manyu</creator><contributor>Raghavan, Balaji</contributor><creatorcontrib>Hou, Junxia ; Lv, Quanyi ; Xiao, Manyu ; Raghavan, Balaji</creatorcontrib><description>Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2014/598716</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Puplishing Corporation</publisher><subject>Algorithms ; Computational efficiency ; Computing time ; Conjugate gradient method ; Control theory ; Efficiency ; Inequalities ; Inverse ; Inverse matrices ; Iterative methods ; Mathematical analysis ; Mathematical models ; Matrix ; Parameter modification</subject><ispartof>Mathematical problems in engineering, 2014-01, Vol.2014 (2014), p.1-7</ispartof><rights>Copyright © 2014 Junxia Hou et al.</rights><rights>Copyright © 2014 Junxia Hou et al. Junxia Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c346t-ea3148eec5583b0f040e2839f3c15b38a352d7ae36af7d2afab396533714af8c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,27929,27930</link.rule.ids></links><search><contributor>Raghavan, Balaji</contributor><creatorcontrib>Hou, Junxia</creatorcontrib><creatorcontrib>Lv, Quanyi</creatorcontrib><creatorcontrib>Xiao, Manyu</creatorcontrib><title>A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation</title><title>Mathematical problems in engineering</title><description>Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency.</description><subject>Algorithms</subject><subject>Computational efficiency</subject><subject>Computing time</subject><subject>Conjugate gradient method</subject><subject>Control theory</subject><subject>Efficiency</subject><subject>Inequalities</subject><subject>Inverse</subject><subject>Inverse matrices</subject><subject>Iterative methods</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Matrix</subject><subject>Parameter modification</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqF0ElLxEAQBeAgCq4nz0KDF1GiXb0knaMMbjCDggreYk1SrT3EtHYSl39vDxEPXjxVHT4ej5cku8CPAbQ-ERzUiS5MDtlKsgE6k6kGla_GnwuVgpAP68lm1y04F6DBbCSPp-wGAzYNNewmUOXb2vXOt1Szma-ddfGZ-HYxPGFP7CJg7ajt2Yz6Z18z6wObYngidvvVvFPXU2Az7IP7ZGdvAy6DtpM1i01HOz93K7k_P7ubXKbT64uryek0raTK-pRQgjJEldZGzrnlipMwsrCyAj2XBqUWdY4kM7R5LdDiXBaZljIHhdZUcis5GHNfg38bYpXyxXUVNQ225IeuBK1AiUIYiHT_D134IbSxXVRZxkVhijyqo1FVwXddIFu-BveC4asEXi7XLpdrl-PaUR-O-tm1NX64f_DeiCkSsviLlVFcZvIbsMiH3w</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Hou, Junxia</creator><creator>Lv, Quanyi</creator><creator>Xiao, Manyu</creator><general>Hindawi Puplishing Corporation</general><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20140101</creationdate><title>A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation</title><author>Hou, Junxia ; Lv, Quanyi ; Xiao, Manyu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c346t-ea3148eec5583b0f040e2839f3c15b38a352d7ae36af7d2afab396533714af8c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Computational efficiency</topic><topic>Computing time</topic><topic>Conjugate gradient method</topic><topic>Control theory</topic><topic>Efficiency</topic><topic>Inequalities</topic><topic>Inverse</topic><topic>Inverse matrices</topic><topic>Iterative methods</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Matrix</topic><topic>Parameter modification</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hou, Junxia</creatorcontrib><creatorcontrib>Lv, Quanyi</creatorcontrib><creatorcontrib>Xiao, Manyu</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</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>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Access via ProQuest (Open Access)</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><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hou, Junxia</au><au>Lv, Quanyi</au><au>Xiao, Manyu</au><au>Raghavan, Balaji</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>2014</volume><issue>2014</issue><spage>1</spage><epage>7</epage><pages>1-7</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Puplishing Corporation</pub><doi>10.1155/2014/598716</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 1024-123X |
ispartof | Mathematical problems in engineering, 2014-01, Vol.2014 (2014), p.1-7 |
issn | 1024-123X 1563-5147 |
language | eng |
recordid | cdi_proquest_miscellaneous_1541429281 |
source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Wiley Online Library (Open Access Collection); Alma/SFX Local Collection |
subjects | Algorithms Computational efficiency Computing time Conjugate gradient method Control theory Efficiency Inequalities Inverse Inverse matrices Iterative methods Mathematical analysis Mathematical models Matrix Parameter modification |
title | A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-11T04%3A10%3A07IST&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=A%20Parallel%20Preconditioned%20Modified%20Conjugate%20Gradient%20Method%20for%20Large%20Sylvester%20Matrix%20Equation&rft.jtitle=Mathematical%20problems%20in%20engineering&rft.au=Hou,%20Junxia&rft.date=2014-01-01&rft.volume=2014&rft.issue=2014&rft.spage=1&rft.epage=7&rft.pages=1-7&rft.issn=1024-123X&rft.eissn=1563-5147&rft_id=info:doi/10.1155/2014/598716&rft_dat=%3Cproquest_cross%3E1541429281%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=1566029897&rft_id=info:pmid/&rfr_iscdi=true |