Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices
In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for Z -matrices, Linear Algebra Appl. 267 (1997) 113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant Z -matrices wi...
Gespeichert in:
| Veröffentlicht in: | Computers & mathematics with applications (1987) 2008-10, Vol.56 (8), p.2048-2053 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2053 |
|---|---|
| container_issue | 8 |
| container_start_page | 2048 |
| container_title | Computers & mathematics with applications (1987) |
| container_volume | 56 |
| creator | Liu, Qingbing Chen, Guoliang Cai, Jing |
| description | In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant
Z
-matrices with a preconditioner
I
+
S
α
is superior to that of the basic iterative method. In this paper, we present a new preconditioner
I
+
K
β
which is different from the preconditioner given by Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an
H
-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given. |
| doi_str_mv | 10.1016/j.camwa.2008.03.033 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_34707839</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0898122108003386</els_id><sourcerecordid>1082202826</sourcerecordid><originalsourceid>FETCH-LOGICAL-c367t-d2bbc4bc7b7a3fc092e35f9e80b94d169729e172eb9edd5c679df40b3f799d663</originalsourceid><addsrcrecordid>eNp9kM1KxDAUhYMoOP48gZusxE3Hm6Q2ycKFDP6BoKCuQ5rcaoa2GZOOMjvfwTf0Sew4roUDd_OdA_cj5IjBlAGrTudTZ7sPO-UAagpijNgiE6akKGRVqW0yAaVVwThnu2Qv5zkAlILDhDzMYv-O6QV7h9T2tl3lkGls6PCKdJHQxd6HIcQePb22y5y_P78eMXhsaYfDa_S0iYne0KKzQwoO8wHZaWyb8fDv7pPnq8un2U1xd399O7u4K5yo5FB4XteurJ2spRWNA81RnDUaFdS69KzSkmtkkmOt0fszV0ntmxJq0UitfVWJfXK82V2k-LbEPJguZIdta3uMy2xEKUEqoUfw5F-QgeIcuOLrTbFBXYo5J2zMIoXOptUImbVoMze_os1atAExRoyt800Lx3ffAyaTXVj79GH0Nxgfw7_9H6e7iRk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1082202826</pqid></control><display><type>article</type><title>Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>ScienceDirect Journals (5 years ago - present)</source><creator>Liu, Qingbing ; Chen, Guoliang ; Cai, Jing</creator><creatorcontrib>Liu, Qingbing ; Chen, Guoliang ; Cai, Jing</creatorcontrib><description>In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant
Z
-matrices with a preconditioner
I
+
S
α
is superior to that of the basic iterative method. In this paper, we present a new preconditioner
I
+
K
β
which is different from the preconditioner given by Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an
H
-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2008.03.033</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>[formula omitted]-matrix ; [formula omitted]-splitting ; Basic converters ; Coefficients ; Convergence ; Gauss-Seidel method ; Iterative methods ; Linear algebra ; Mathematical models ; Preconditioned iterative method ; Preconditioner</subject><ispartof>Computers & mathematics with applications (1987), 2008-10, Vol.56 (8), p.2048-2053</ispartof><rights>2008</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c367t-d2bbc4bc7b7a3fc092e35f9e80b94d169729e172eb9edd5c679df40b3f799d663</citedby><cites>FETCH-LOGICAL-c367t-d2bbc4bc7b7a3fc092e35f9e80b94d169729e172eb9edd5c679df40b3f799d663</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.camwa.2008.03.033$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3548,27922,27923,45993</link.rule.ids></links><search><creatorcontrib>Liu, Qingbing</creatorcontrib><creatorcontrib>Chen, Guoliang</creatorcontrib><creatorcontrib>Cai, Jing</creatorcontrib><title>Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices</title><title>Computers & mathematics with applications (1987)</title><description>In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant
Z
-matrices with a preconditioner
I
+
S
α
is superior to that of the basic iterative method. In this paper, we present a new preconditioner
I
+
K
β
which is different from the preconditioner given by Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an
H
-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given.</description><subject>[formula omitted]-matrix</subject><subject>[formula omitted]-splitting</subject><subject>Basic converters</subject><subject>Coefficients</subject><subject>Convergence</subject><subject>Gauss-Seidel method</subject><subject>Iterative methods</subject><subject>Linear algebra</subject><subject>Mathematical models</subject><subject>Preconditioned iterative method</subject><subject>Preconditioner</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KxDAUhYMoOP48gZusxE3Hm6Q2ycKFDP6BoKCuQ5rcaoa2GZOOMjvfwTf0Sew4roUDd_OdA_cj5IjBlAGrTudTZ7sPO-UAagpijNgiE6akKGRVqW0yAaVVwThnu2Qv5zkAlILDhDzMYv-O6QV7h9T2tl3lkGls6PCKdJHQxd6HIcQePb22y5y_P78eMXhsaYfDa_S0iYne0KKzQwoO8wHZaWyb8fDv7pPnq8un2U1xd399O7u4K5yo5FB4XteurJ2spRWNA81RnDUaFdS69KzSkmtkkmOt0fszV0ntmxJq0UitfVWJfXK82V2k-LbEPJguZIdta3uMy2xEKUEqoUfw5F-QgeIcuOLrTbFBXYo5J2zMIoXOptUImbVoMze_os1atAExRoyt800Lx3ffAyaTXVj79GH0Nxgfw7_9H6e7iRk</recordid><startdate>20081001</startdate><enddate>20081001</enddate><creator>Liu, Qingbing</creator><creator>Chen, Guoliang</creator><creator>Cai, Jing</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20081001</creationdate><title>Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices</title><author>Liu, Qingbing ; Chen, Guoliang ; Cai, Jing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c367t-d2bbc4bc7b7a3fc092e35f9e80b94d169729e172eb9edd5c679df40b3f799d663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>[formula omitted]-matrix</topic><topic>[formula omitted]-splitting</topic><topic>Basic converters</topic><topic>Coefficients</topic><topic>Convergence</topic><topic>Gauss-Seidel method</topic><topic>Iterative methods</topic><topic>Linear algebra</topic><topic>Mathematical models</topic><topic>Preconditioned iterative method</topic><topic>Preconditioner</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Qingbing</creatorcontrib><creatorcontrib>Chen, Guoliang</creatorcontrib><creatorcontrib>Cai, Jing</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Qingbing</au><au>Chen, Guoliang</au><au>Cai, Jing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2008-10-01</date><risdate>2008</risdate><volume>56</volume><issue>8</issue><spage>2048</spage><epage>2053</epage><pages>2048-2053</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant
Z
-matrices with a preconditioner
I
+
S
α
is superior to that of the basic iterative method. In this paper, we present a new preconditioner
I
+
K
β
which is different from the preconditioner given by Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss–Seidel method for
Z
-matrices, Linear Algebra Appl. 267 (1997) 113–123] and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an
H
-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2008.03.033</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0898-1221 |
| ispartof | Computers & mathematics with applications (1987), 2008-10, Vol.56 (8), p.2048-2053 |
| issn | 0898-1221 1873-7668 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_34707839 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | [formula omitted]-matrix [formula omitted]-splitting Basic converters Coefficients Convergence Gauss-Seidel method Iterative methods Linear algebra Mathematical models Preconditioned iterative method Preconditioner |
| title | Convergence analysis of the preconditioned Gauss–Seidel method for H -matrices |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T00%3A54%3A14IST&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=Convergence%20analysis%20of%20the%20preconditioned%20Gauss%E2%80%93Seidel%20method%20for%20H%20-matrices&rft.jtitle=Computers%20&%20mathematics%20with%20applications%20(1987)&rft.au=Liu,%20Qingbing&rft.date=2008-10-01&rft.volume=56&rft.issue=8&rft.spage=2048&rft.epage=2053&rft.pages=2048-2053&rft.issn=0898-1221&rft.eissn=1873-7668&rft_id=info:doi/10.1016/j.camwa.2008.03.033&rft_dat=%3Cproquest_cross%3E1082202826%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=1082202826&rft_id=info:pmid/&rft_els_id=S0898122108003386&rfr_iscdi=true |