Orthogonal reduction of dense matrices to bidiagonal form on computers with distributed memory architectures
In this paper, we describe a parallel implementation for the blocked reduction of dense matrices to bidiagonal form by Householder transformations. The method is based on the idea of using un-normed reflector vector. Results from experiments on the Intel Paragon are given. Comparison between the Sca...
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| Published in: | Parallel computing Vol. 24; no. 2; pp. 305 - 313 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.02.1998
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| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | In this paper, we describe a parallel implementation for the blocked reduction of dense matrices to bidiagonal form by Householder transformations. The method is based on the idea of using un-normed reflector vector. Results from experiments on the Intel Paragon are given. Comparison between the ScaLapack bidiagonalization and the method proposed is provided. |
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| AbstractList | In this paper, we describe a parallel implementation for the blocked reduction of dense matrices to bidiagonal form by Householder transformations. The method is based on the idea of using un-normed reflector vector. Results from experiments on the Intel Paragon are given. Comparison between the ScaLapack bidiagonalization and the method proposed is provided. |
| Author | Kuznetsov, S.V. |
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| Cites_doi | 10.1007/3-540-60902-4_12 10.1137/0908009 10.1017/S096249290000235X 10.1007/978-94-011-1952-8 10.1016/0167-8191(92)90011-U |
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| Keywords | Bidiagonal form Distributed memory architecture Linear algebra Householder transformation |
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| References | A.N. Malyshev, Development of parallel codes based on bidiagonalization for MIMD architecture, IRISA, Research report No. 961, October 1995. J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R.C. Whaley, Installation Guide for ScaLapack (Version 1.0), University of Tennessee, CS-95-280, 1995. G.H. Golub, C.F. van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, 1989. Bishof, van Loan (BIB2) 1987; 8 Dongarra, van de Geijn (BIB6) 1992; 18 S.K. Godunov, A.G. Antonov, O.P. Kirilyuck, V.I. Kostin, Guaranteed Accuracy in Numerical Linear Algebra, Kluwer Academic Publ., Dordrecht, 1993. J. Demmel, M. Heath, Henk A. van der Vorst, Parallel Numerical Linear Algebra, University of Tennessee, CS-93-192, 1993. J. Dongarra, R.C. Whaley, A User's Guide to the BLACS v1.0, LAPACK Working Note N 94, University of Tennessee, 1995. A.G. Antonov, An algorithm of reduction of matrix to bidiagonal form, in: S. Godunov (Ed.), Numerical Methods of Linear Algebra, Transactions of Institute of Mathematics 6, Novosibirks, Nauka, 1985, pp. 182–191. J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R.C. Whaley, ScaLapack: A Portable Linear Algebra Library for Distributed Memory Computers—Design Issues and Performance, University of Tennessee, CS-95-283, 1995. Bishof (10.1016/S0167-8191(98)00008-8_BIB2) 1987; 8 Dongarra (10.1016/S0167-8191(98)00008-8_BIB6) 1992; 18 10.1016/S0167-8191(98)00008-8_BIB9 10.1016/S0167-8191(98)00008-8_BIB8 10.1016/S0167-8191(98)00008-8_BIB1 10.1016/S0167-8191(98)00008-8_BIB3 10.1016/S0167-8191(98)00008-8_BIB5 10.1016/S0167-8191(98)00008-8_BIB4 10.1016/S0167-8191(98)00008-8_BIB10 10.1016/S0167-8191(98)00008-8_BIB7 |
| References_xml | – reference: A.N. Malyshev, Development of parallel codes based on bidiagonalization for MIMD architecture, IRISA, Research report No. 961, October 1995. – volume: 8 start-page: 2 year: 1987 end-page: 13 ident: BIB2 article-title: The wy representation for product of householder matrices publication-title: SIAM J. Sci. Stat. Comput. – reference: A.G. Antonov, An algorithm of reduction of matrix to bidiagonal form, in: S. Godunov (Ed.), Numerical Methods of Linear Algebra, Transactions of Institute of Mathematics 6, Novosibirks, Nauka, 1985, pp. 182–191. – reference: J. Demmel, M. Heath, Henk A. van der Vorst, Parallel Numerical Linear Algebra, University of Tennessee, CS-93-192, 1993. – volume: 18 start-page: 973 year: 1992 end-page: 982 ident: BIB6 article-title: Reduction to condensed form for the eigenvalue problem on distributed memory architectures publication-title: Parallel Comput. – reference: J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R.C. Whaley, Installation Guide for ScaLapack (Version 1.0), University of Tennessee, CS-95-280, 1995. – reference: S.K. Godunov, A.G. Antonov, O.P. Kirilyuck, V.I. Kostin, Guaranteed Accuracy in Numerical Linear Algebra, Kluwer Academic Publ., Dordrecht, 1993. – reference: J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R.C. Whaley, ScaLapack: A Portable Linear Algebra Library for Distributed Memory Computers—Design Issues and Performance, University of Tennessee, CS-95-283, 1995. – reference: G.H. Golub, C.F. van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, 1989. – reference: J. Dongarra, R.C. Whaley, A User's Guide to the BLACS v1.0, LAPACK Working Note N 94, University of Tennessee, 1995. – ident: 10.1016/S0167-8191(98)00008-8_BIB4 doi: 10.1007/3-540-60902-4_12 – ident: 10.1016/S0167-8191(98)00008-8_BIB9 – volume: 8 start-page: 2 year: 1987 ident: 10.1016/S0167-8191(98)00008-8_BIB2 article-title: The wy representation for product of householder matrices publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0908009 – ident: 10.1016/S0167-8191(98)00008-8_BIB7 doi: 10.1017/S096249290000235X – ident: 10.1016/S0167-8191(98)00008-8_BIB8 doi: 10.1007/978-94-011-1952-8 – ident: 10.1016/S0167-8191(98)00008-8_BIB3 doi: 10.1007/3-540-60902-4_12 – volume: 18 start-page: 973 year: 1992 ident: 10.1016/S0167-8191(98)00008-8_BIB6 article-title: Reduction to condensed form for the eigenvalue problem on distributed memory architectures publication-title: Parallel Comput. doi: 10.1016/0167-8191(92)90011-U – ident: 10.1016/S0167-8191(98)00008-8_BIB5 – ident: 10.1016/S0167-8191(98)00008-8_BIB10 – ident: 10.1016/S0167-8191(98)00008-8_BIB1 |
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| SubjectTerms | Bidiagonal form Distributed memory architecture Householder transformation Linear algebra |
| Title | Orthogonal reduction of dense matrices to bidiagonal form on computers with distributed memory architectures |
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