Fast approximate truncated SVD
Summary This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conv...
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| Veröffentlicht in: | Numerical linear algebra with applications 2019-08, Vol.26 (4), p.n/a |
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| container_title | Numerical linear algebra with applications |
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| creator | Shishkin, Serge L. Shalaginov, Arkadi Bopardikar, Shaunak D. |
| description | Summary
This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method. |
| doi_str_mv | 10.1002/nla.2246 |
| format | Article |
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This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.</description><identifier>ISSN: 1070-5325</identifier><identifier>EISSN: 1099-1506</identifier><identifier>DOI: 10.1002/nla.2246</identifier><language>eng</language><publisher>Oxford: Wiley Subscription Services, Inc</publisher><subject>Asymptotic methods ; Asymptotic properties ; Computer simulation ; incremental computation ; matrix factorization ; Methods ; Parallel processing ; Randomization ; scalability ; Singular value decomposition</subject><ispartof>Numerical linear algebra with applications, 2019-08, Vol.26 (4), p.n/a</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2936-c8b20da5c243bee28f38c7f94cdaf40f013db9e1d5dc2ad90aeba15c8dd10b03</citedby><cites>FETCH-LOGICAL-c2936-c8b20da5c243bee28f38c7f94cdaf40f013db9e1d5dc2ad90aeba15c8dd10b03</cites><orcidid>0000-0002-9864-030X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnla.2246$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnla.2246$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1416,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Shishkin, Serge L.</creatorcontrib><creatorcontrib>Shalaginov, Arkadi</creatorcontrib><creatorcontrib>Bopardikar, Shaunak D.</creatorcontrib><title>Fast approximate truncated SVD</title><title>Numerical linear algebra with applications</title><description>Summary
This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.</description><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Computer simulation</subject><subject>incremental computation</subject><subject>matrix factorization</subject><subject>Methods</subject><subject>Parallel processing</subject><subject>Randomization</subject><subject>scalability</subject><subject>Singular value decomposition</subject><issn>1070-5325</issn><issn>1099-1506</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1j0tLw0AUhQdRsFbBXyABN26m3nmlmWWpVoWgC4vbYTIPaIlJnEnQ_vtOjFtX9yw-zj0fQtcEFgSA3je1XlDK8xM0IyAlJgLy0zEvAQtGxTm6iHEPALmQbIZuNjr2me660P7sPnXvsj4MjUnBZu8fD5fozOs6uqu_O0fbzeN2_YzLt6eX9arEhkqWY1NUFKwWhnJWOUcLzwqz9JIbqz0HD4TZSjpihTVUWwnaVZoIU1hLoAI2R7dTbZrxNbjYq307hCZ9VJQK4DwHEIm6mygT2hiD86oLaXM4KAJqlFdJXo3yCcUT-r2r3eFfTr2Wq1_-COP_WaA</recordid><startdate>201908</startdate><enddate>201908</enddate><creator>Shishkin, Serge L.</creator><creator>Shalaginov, Arkadi</creator><creator>Bopardikar, Shaunak D.</creator><general>Wiley Subscription Services, Inc</general><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><orcidid>https://orcid.org/0000-0002-9864-030X</orcidid></search><sort><creationdate>201908</creationdate><title>Fast approximate truncated SVD</title><author>Shishkin, Serge L. ; Shalaginov, Arkadi ; Bopardikar, Shaunak D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2936-c8b20da5c243bee28f38c7f94cdaf40f013db9e1d5dc2ad90aeba15c8dd10b03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic properties</topic><topic>Computer simulation</topic><topic>incremental computation</topic><topic>matrix factorization</topic><topic>Methods</topic><topic>Parallel processing</topic><topic>Randomization</topic><topic>scalability</topic><topic>Singular value decomposition</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shishkin, Serge L.</creatorcontrib><creatorcontrib>Shalaginov, Arkadi</creatorcontrib><creatorcontrib>Bopardikar, Shaunak D.</creatorcontrib><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>Numerical linear algebra with applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shishkin, Serge L.</au><au>Shalaginov, Arkadi</au><au>Bopardikar, Shaunak D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fast approximate truncated SVD</atitle><jtitle>Numerical linear algebra with applications</jtitle><date>2019-08</date><risdate>2019</risdate><volume>26</volume><issue>4</issue><epage>n/a</epage><issn>1070-5325</issn><eissn>1099-1506</eissn><abstract>Summary
This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.</abstract><cop>Oxford</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/nla.2246</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-9864-030X</orcidid></addata></record> |
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| ispartof | Numerical linear algebra with applications, 2019-08, Vol.26 (4), p.n/a |
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| language | eng |
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| subjects | Asymptotic methods Asymptotic properties Computer simulation incremental computation matrix factorization Methods Parallel processing Randomization scalability Singular value decomposition |
| title | Fast approximate truncated SVD |
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