Using semiseparable matrices to compute the SVD of a general matrix product/quotient
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| Title: | Using semiseparable matrices to compute the SVD of a general matrix product/quotient |
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| Authors: | Van Barel, Marc1 marc.vanbarel@cs.kuleuven.be, Vanberghen, Yvette1 yvette.vanberghen@cs.kuleuven.be, Van Dooren, Paul2 paul.vandooren@uclouvain.be |
| Source: | Journal of Computational & Applied Mathematics. Oct2010, Vol. 234 Issue 11, p3175-3180. 6p. |
| Subjects: | Semiseparable matrices, Singular value decomposition, Iterative methods (Mathematics), Algorithms, Mathematical analysis |
| Abstract: | Abstract: In this work we reduce the computation of the singular values of a general product/quotient of matrices to the computation of the singular values of an upper triangular semiseparable matrix. Compared to the reduction into a bidiagonal matrix the reduction into semiseparable form exhibits a nested subspace iteration. Hence, when there are large gaps between the singular values, these gaps manifest themselves already during the reduction algorithm in contrast to the bidiagonal case. [Copyright &y& Elsevier] |
| Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 52205384 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Using semiseparable matrices to compute the SVD of a general matrix product/quotient – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Van+Barel%2C+Marc%22">Van Barel, Marc</searchLink><relatesTo>1</relatesTo><i> marc.vanbarel@cs.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22Vanberghen%2C+Yvette%22">Vanberghen, Yvette</searchLink><relatesTo>1</relatesTo><i> yvette.vanberghen@cs.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22Van+Dooren%2C+Paul%22">Van Dooren, Paul</searchLink><relatesTo>2</relatesTo><i> paul.vandooren@uclouvain.be</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Applied+Mathematics%22">Journal of Computational & Applied Mathematics</searchLink>. Oct2010, Vol. 234 Issue 11, p3175-3180. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Semiseparable+matrices%22">Semiseparable matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Singular+value+decomposition%22">Singular value decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: In this work we reduce the computation of the singular values of a general product/quotient of matrices to the computation of the singular values of an upper triangular semiseparable matrix. Compared to the reduction into a bidiagonal matrix the reduction into semiseparable form exhibits a nested subspace iteration. Hence, when there are large gaps between the singular values, these gaps manifest themselves already during the reduction algorithm in contrast to the bidiagonal case. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.cam.2010.02.007 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 3175 Subjects: – SubjectFull: Semiseparable matrices Type: general – SubjectFull: Singular value decomposition Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Using semiseparable matrices to compute the SVD of a general matrix product/quotient Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Van Barel, Marc – PersonEntity: Name: NameFull: Vanberghen, Yvette – PersonEntity: Name: NameFull: Van Dooren, Paul IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 03770427 Numbering: – Type: volume Value: 234 – Type: issue Value: 11 Titles: – TitleFull: Journal of Computational & Applied Mathematics Type: main |
| ResultId | 1 |
