ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES.
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| Title: | ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES. |
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| Authors: | Pelaez, Maria Jose1 mpelaez@math.uc3m.es, Moro, Julio1 jmoro@math.uc3m.es |
| Source: | SIAM Journal on Matrix Analysis & Applications. 2006, Vol. 28 Issue 4, p1173-1198. 26p. 4 Charts, 1 Graph. |
| Subjects: | Factorization, Factorization of operators, Eigenvalues, Matrices (Mathematics), Symmetric functions, Symmetric matrices |
| Abstract: | Two algorithms are presented which compute, with small componentwise relative error, a block LDLT factorization of symmetric matrices belonging to two classes of matrices: diagonally scaled totally unimodular (DSTU) and total signed compound (TSC) matrices. This accuracy is achieved by taking advantage of some special properties of such structures in order to avoid subtractions throughout the factorization process. Once an accurate block LDLT decomposition is available, it is proved that one can easily obtain an accurate symmetric rank-revealing decomposition, which is the starting point for algorithms computing with high relative accuracy the eigenvalues and eigenvectors of arbitrary, possibly indefinite, symmetric matrices. This proves that eigenvalues and eigenvectors of symmetric DSTU and TSC matrices can be computed with high relative accuracy. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Matrix Analysis & Applications is the property of Society for Industrial & Applied Mathematics 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pelaez%2C+Maria+Jose%22">Pelaez, Maria Jose</searchLink><relatesTo>1</relatesTo><i> mpelaez@math.uc3m.es</i><br /><searchLink fieldCode="AR" term="%22Moro%2C+Julio%22">Moro, Julio</searchLink><relatesTo>1</relatesTo><i> jmoro@math.uc3m.es</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Matrix+Analysis+%26+Applications%22">SIAM Journal on Matrix Analysis & Applications</searchLink>. 2006, Vol. 28 Issue 4, p1173-1198. 26p. 4 Charts, 1 Graph. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization+of+operators%22">Factorization of operators</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetric+functions%22">Symmetric functions</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetric+matrices%22">Symmetric matrices</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Two algorithms are presented which compute, with small componentwise relative error, a block LDLT factorization of symmetric matrices belonging to two classes of matrices: diagonally scaled totally unimodular (DSTU) and total signed compound (TSC) matrices. This accuracy is achieved by taking advantage of some special properties of such structures in order to avoid subtractions throughout the factorization process. Once an accurate block LDLT decomposition is available, it is proved that one can easily obtain an accurate symmetric rank-revealing decomposition, which is the starting point for algorithms computing with high relative accuracy the eigenvalues and eigenvectors of arbitrary, possibly indefinite, symmetric matrices. This proves that eigenvalues and eigenvectors of symmetric DSTU and TSC matrices can be computed with high relative accuracy. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Matrix Analysis & Applications is the property of Society for Industrial & Applied Mathematics 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: 10.1137/050631537 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 26 StartPage: 1173 Subjects: – SubjectFull: Factorization Type: general – SubjectFull: Factorization of operators Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Symmetric functions Type: general – SubjectFull: Symmetric matrices Type: general Titles: – TitleFull: ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pelaez, Maria Jose – PersonEntity: Name: NameFull: Moro, Julio IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: 2006 Type: published Y: 2006 Identifiers: – Type: issn-print Value: 08954798 Numbering: – Type: volume Value: 28 – Type: issue Value: 4 Titles: – TitleFull: SIAM Journal on Matrix Analysis & Applications Type: main |
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