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A fast and stable algorithm for downdating the singular value decomposition.

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Title: A fast and stable algorithm for downdating the singular value decomposition.
Authors: Zhang, Jieyuan1,2, Li, Shengguo3 nudtlsg@nudt.edu.cn, Cheng, Lizhi1,2, Liao, Xiangke3, Cheng, Guangquan4
Source: Computers & Mathematics with Applications. Nov2014, Vol. 68 Issue 10, p1421-1430. 10p.
Subjects: Singular value decomposition, Semiseparable matrices, Mathematical programming, Approximation theory, Eigenvectors, Matrix multiplications
Abstract: In this paper, we modify a classical downdating SVD algorithm and reduce its complexity significantly. We use a structured low-rank approximation algorithm to compute an hierarchically semiseparable (HSS) matrix approximation to the eigenvector matrix of a diagonal matrix plus rank-one modification. The complexity of our downdating algorithm is analyzed. We further show that the structured low-rank approximation algorithm is backward stable. Numerous experiments have been done to show the efficiency of our algorithm. For some matrices with large dimensions, our algorithm can be much faster than that using plain matrix–matrix multiplication routine in Intel MKL in both sequential and parallel cases. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 99198102
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Jieyuan%22">Zhang, Jieyuan</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Li%2C+Shengguo%22">Li, Shengguo</searchLink><relatesTo>3</relatesTo><i> nudtlsg@nudt.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Cheng%2C+Lizhi%22">Cheng, Lizhi</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Liao%2C+Xiangke%22">Liao, Xiangke</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Cheng%2C+Guangquan%22">Cheng, Guangquan</searchLink><relatesTo>4</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Nov2014, Vol. 68 Issue 10, p1421-1430. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Singular+value+decomposition%22">Singular value decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Semiseparable+matrices%22">Semiseparable matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvectors%22">Eigenvectors</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+multiplications%22">Matrix multiplications</searchLink>
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  Label: Abstract
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  Data: In this paper, we modify a classical downdating SVD algorithm and reduce its complexity significantly. We use a structured low-rank approximation algorithm to compute an hierarchically semiseparable (HSS) matrix approximation to the eigenvector matrix of a diagonal matrix plus rank-one modification. The complexity of our downdating algorithm is analyzed. We further show that the structured low-rank approximation algorithm is backward stable. Numerous experiments have been done to show the efficiency of our algorithm. For some matrices with large dimensions, our algorithm can be much faster than that using plain matrix–matrix multiplication routine in Intel MKL in both sequential and parallel cases. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.camwa.2014.09.008
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        Text: English
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        PageCount: 10
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      – SubjectFull: Singular value decomposition
        Type: general
      – SubjectFull: Semiseparable matrices
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      – SubjectFull: Mathematical programming
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      – SubjectFull: Approximation theory
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      – SubjectFull: Eigenvectors
        Type: general
      – SubjectFull: Matrix multiplications
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              Text: Nov2014
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