A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems
Based on the variant of the deteriorated positive-definite and skew-Hermitian splitting (VDPSS) preconditioner developed by Zhang and Gu (BIT Numer. Math. 56:587–604, 2016 ), a generalized VDPSS (GVDPSS) preconditioner is established in this paper by replacing the parameter α in (2,2)-block of the V...
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| Veröffentlicht in: | Numerical algorithms 2017-08, Vol.75 (4), p.1161-1191 |
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| creator | Huang, Zheng-Ge Wang, Li-Gong Xu, Zhong Cui, Jing-Jing |
| description | Based on the variant of the deteriorated positive-definite and skew-Hermitian splitting (VDPSS) preconditioner developed by Zhang and Gu (BIT Numer. Math. 56:587–604,
2016
), a generalized VDPSS (GVDPSS) preconditioner is established in this paper by replacing the parameter
α
in (2,2)-block of the VDPSS preconditioner by another parameter
β
. This preconditioner can also be viewed as a generalized form of the VDPSS preconditioner and the new relaxed HSS (NRHSS) preconditioner which has been exhibited by Salkuyeh and Masoudi (Numer. Algorithms,
2016
). The convergence properties of the GVDPSS iteration method are derived. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analyzed in detail. We also study the upper bounds on the degree of the minimum polynomial of the preconditioned matrix. Numerical experiments are implemented to illustrate the effectiveness of the GVDPSS preconditioner and verify that the GVDPSS preconditioned generalized minimal residual method is superior to the DPSS, relaxed DPSS, SIMPLE-like, NRHSS, and VDPSS preconditioned ones for solving saddle point problems in terms of the iterations and computational times. |
| doi_str_mv | 10.1007/s11075-016-0236-2 |
| format | Article |
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2016
), a generalized VDPSS (GVDPSS) preconditioner is established in this paper by replacing the parameter
α
in (2,2)-block of the VDPSS preconditioner by another parameter
β
. This preconditioner can also be viewed as a generalized form of the VDPSS preconditioner and the new relaxed HSS (NRHSS) preconditioner which has been exhibited by Salkuyeh and Masoudi (Numer. Algorithms,
2016
). The convergence properties of the GVDPSS iteration method are derived. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analyzed in detail. We also study the upper bounds on the degree of the minimum polynomial of the preconditioned matrix. Numerical experiments are implemented to illustrate the effectiveness of the GVDPSS preconditioner and verify that the GVDPSS preconditioned generalized minimal residual method is superior to the DPSS, relaxed DPSS, SIMPLE-like, NRHSS, and VDPSS preconditioned ones for solving saddle point problems in terms of the iterations and computational times.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-016-0236-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Approximation ; Computer Science ; Eigenvalues ; Eigenvectors ; Iterative methods ; Methods ; Numeric Computing ; Numerical Analysis ; Original Paper ; Parameters ; Polynomials ; Saddle points ; Theory of Computation ; Upper bounds</subject><ispartof>Numerical algorithms, 2017-08, Vol.75 (4), p.1161-1191</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Springer Science+Business Media New York 2016.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-7b2eda3e463bfed48a797fa0458354e3d6ee36267cd17cff6db8ebb9fd5dac1d3</citedby><cites>FETCH-LOGICAL-c316t-7b2eda3e463bfed48a797fa0458354e3d6ee36267cd17cff6db8ebb9fd5dac1d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-016-0236-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-016-0236-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Huang, Zheng-Ge</creatorcontrib><creatorcontrib>Wang, Li-Gong</creatorcontrib><creatorcontrib>Xu, Zhong</creatorcontrib><creatorcontrib>Cui, Jing-Jing</creatorcontrib><title>A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>Based on the variant of the deteriorated positive-definite and skew-Hermitian splitting (VDPSS) preconditioner developed by Zhang and Gu (BIT Numer. Math. 56:587–604,
2016
), a generalized VDPSS (GVDPSS) preconditioner is established in this paper by replacing the parameter
α
in (2,2)-block of the VDPSS preconditioner by another parameter
β
. This preconditioner can also be viewed as a generalized form of the VDPSS preconditioner and the new relaxed HSS (NRHSS) preconditioner which has been exhibited by Salkuyeh and Masoudi (Numer. Algorithms,
2016
). The convergence properties of the GVDPSS iteration method are derived. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analyzed in detail. We also study the upper bounds on the degree of the minimum polynomial of the preconditioned matrix. Numerical experiments are implemented to illustrate the effectiveness of the GVDPSS preconditioner and verify that the GVDPSS preconditioned generalized minimal residual method is superior to the DPSS, relaxed DPSS, SIMPLE-like, NRHSS, and VDPSS preconditioned ones for solving saddle point problems in terms of the iterations and computational times.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Computer Science</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Iterative methods</subject><subject>Methods</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Parameters</subject><subject>Polynomials</subject><subject>Saddle points</subject><subject>Theory of Computation</subject><subject>Upper bounds</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kE1LAzEQhoMoWKs_wFvA82o-dpPdYyl-QUGheg7ZzaSm7G7WJBXqrzelgidPMzDv8w48CF1TcksJkXeRUiKrglBREMZFwU7QjFaSFQ0T1WneCZUF5U19ji5i3BKSKSZnqFvgDYwQdO--weAvHZweE_YWpw_ABhIE54NO-fa6XuMpQOdH45LzGcLWBzz6Me6HAVJwHY7amB7w5F0umYJvexjiJTqzuo9w9Tvn6P3h_m35VKxeHp-Xi1XRcSpSIVsGRnMoBW8tmLLWspFWk7KqeVUCNwKACyZkZ6jsrBWmraFtG2sqoztq-BzdHHvz488dxKS2fhfG_FKxhtYZLRueU_SY6oKPMYBVU3CDDntFiTq4VEeXKrtUB5eKZYYdmZiz4wbCX_P_0A-l7Hl3</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Huang, Zheng-Ge</creator><creator>Wang, Li-Gong</creator><creator>Xu, Zhong</creator><creator>Cui, Jing-Jing</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20170801</creationdate><title>A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems</title><author>Huang, Zheng-Ge ; Wang, Li-Gong ; Xu, Zhong ; Cui, Jing-Jing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-7b2eda3e463bfed48a797fa0458354e3d6ee36267cd17cff6db8ebb9fd5dac1d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Approximation</topic><topic>Computer Science</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Iterative methods</topic><topic>Methods</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Parameters</topic><topic>Polynomials</topic><topic>Saddle points</topic><topic>Theory of Computation</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Zheng-Ge</creatorcontrib><creatorcontrib>Wang, Li-Gong</creatorcontrib><creatorcontrib>Xu, Zhong</creatorcontrib><creatorcontrib>Cui, Jing-Jing</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</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>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Zheng-Ge</au><au>Wang, Li-Gong</au><au>Xu, Zhong</au><au>Cui, Jing-Jing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2017-08-01</date><risdate>2017</risdate><volume>75</volume><issue>4</issue><spage>1161</spage><epage>1191</epage><pages>1161-1191</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>Based on the variant of the deteriorated positive-definite and skew-Hermitian splitting (VDPSS) preconditioner developed by Zhang and Gu (BIT Numer. Math. 56:587–604,
2016
), a generalized VDPSS (GVDPSS) preconditioner is established in this paper by replacing the parameter
α
in (2,2)-block of the VDPSS preconditioner by another parameter
β
. This preconditioner can also be viewed as a generalized form of the VDPSS preconditioner and the new relaxed HSS (NRHSS) preconditioner which has been exhibited by Salkuyeh and Masoudi (Numer. Algorithms,
2016
). The convergence properties of the GVDPSS iteration method are derived. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analyzed in detail. We also study the upper bounds on the degree of the minimum polynomial of the preconditioned matrix. Numerical experiments are implemented to illustrate the effectiveness of the GVDPSS preconditioner and verify that the GVDPSS preconditioned generalized minimal residual method is superior to the DPSS, relaxed DPSS, SIMPLE-like, NRHSS, and VDPSS preconditioned ones for solving saddle point problems in terms of the iterations and computational times.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-016-0236-2</doi><tpages>31</tpages></addata></record> |
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| subjects | Algebra Algorithms Approximation Computer Science Eigenvalues Eigenvectors Iterative methods Methods Numeric Computing Numerical Analysis Original Paper Parameters Polynomials Saddle points Theory of Computation Upper bounds |
| title | A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems |
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