A block Cholesky-LU-based QR factorization for rectangular matrices
The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or struc...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Le Borne, Sabine [verfasserIn] |
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| Körperschaften: |
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Rechteinformationen: |
Open Access Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International ; CC BY-NC-ND 4.0 |
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| Schlagwörter: |
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| Anmerkung: |
Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik |
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| Umfang: |
Diagramme |
| Übergeordnetes Werk: |
Enthalten in: Numerical linear algebra with applications - New York, NY [u.a.] : Wiley, 1994, 00(2023), 0, Seite 1-10 |
|---|---|
| Übergeordnetes Werk: |
volume:00 ; year:2023 ; number:0 ; pages:1-10 |
| Links: |
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| DOI / URN: |
urn:nbn:de:gbv:830-882.0215239 10.15480/882.5036 10.1002/nla.2497 |
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| Katalog-ID: |
1841110280 |
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| 520 | |a The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. | ||
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urn:nbn:de:gbv:830-882.0215239 urn 10.15480/882.5036 doi 10.1002/nla.2497 doi 11420/15087 hdl (DE-627)1841110280 (DE-599)KXP1841110280 DE-627 ger DE-627 rda eng 510: Mathematik Le Borne, Sabine verfasserin (DE-588)1162159316 (DE-627)1025603109 (DE-576)507230957 aut A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. DE-830 Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International CC BY-NC-ND 4.0 cc https://creativecommons.org/licenses/by-nc-nd/4.0/ block QR factorization DSpace Householder method DSpace Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Numerical linear algebra with applications New York, NY [u.a.] : Wiley, 1994 00(2023), 0, Seite 1-10 Online-Ressource (DE-627)318472139 (DE-600)2012602-5 (DE-576)11461766X 1099-1506 nnns volume:00 year:2023 number:0 pages:1-10 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215239 Resolving-System kostenfrei https://doi.org/10.15480/882.5036 Resolving-System kostenfrei http://hdl.handle.net/11420/15087 Resolving-System kostenfrei https://doi.org/10.1002/nla.2497 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 0 1-10 045F 510: Mathematik 23 01 0830 4301528644 Opus Elektronischer Volltext f z 04-04-23 23 01 0830 https://doi.org/10.15480/882.5036 LF 23 01 0830 Opus 23 01 0830 tubdok 23 01 0830 tuhh |
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urn:nbn:de:gbv:830-882.0215239 urn 10.15480/882.5036 doi 10.1002/nla.2497 doi 11420/15087 hdl (DE-627)1841110280 (DE-599)KXP1841110280 DE-627 ger DE-627 rda eng 510: Mathematik Le Borne, Sabine verfasserin (DE-588)1162159316 (DE-627)1025603109 (DE-576)507230957 aut A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. DE-830 Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International CC BY-NC-ND 4.0 cc https://creativecommons.org/licenses/by-nc-nd/4.0/ block QR factorization DSpace Householder method DSpace Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Numerical linear algebra with applications New York, NY [u.a.] : Wiley, 1994 00(2023), 0, Seite 1-10 Online-Ressource (DE-627)318472139 (DE-600)2012602-5 (DE-576)11461766X 1099-1506 nnns volume:00 year:2023 number:0 pages:1-10 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215239 Resolving-System kostenfrei https://doi.org/10.15480/882.5036 Resolving-System kostenfrei http://hdl.handle.net/11420/15087 Resolving-System kostenfrei https://doi.org/10.1002/nla.2497 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 0 1-10 045F 510: Mathematik 23 01 0830 4301528644 Opus Elektronischer Volltext f z 04-04-23 23 01 0830 https://doi.org/10.15480/882.5036 LF 23 01 0830 Opus 23 01 0830 tubdok 23 01 0830 tuhh |
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urn:nbn:de:gbv:830-882.0215239 urn 10.15480/882.5036 doi 10.1002/nla.2497 doi 11420/15087 hdl (DE-627)1841110280 (DE-599)KXP1841110280 DE-627 ger DE-627 rda eng 510: Mathematik Le Borne, Sabine verfasserin (DE-588)1162159316 (DE-627)1025603109 (DE-576)507230957 aut A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. DE-830 Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International CC BY-NC-ND 4.0 cc https://creativecommons.org/licenses/by-nc-nd/4.0/ block QR factorization DSpace Householder method DSpace Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Numerical linear algebra with applications New York, NY [u.a.] : Wiley, 1994 00(2023), 0, Seite 1-10 Online-Ressource (DE-627)318472139 (DE-600)2012602-5 (DE-576)11461766X 1099-1506 nnns volume:00 year:2023 number:0 pages:1-10 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215239 Resolving-System kostenfrei https://doi.org/10.15480/882.5036 Resolving-System kostenfrei http://hdl.handle.net/11420/15087 Resolving-System kostenfrei https://doi.org/10.1002/nla.2497 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 0 1-10 045F 510: Mathematik 23 01 0830 4301528644 Opus Elektronischer Volltext f z 04-04-23 23 01 0830 https://doi.org/10.15480/882.5036 LF 23 01 0830 Opus 23 01 0830 tubdok 23 01 0830 tuhh |
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urn:nbn:de:gbv:830-882.0215239 urn 10.15480/882.5036 doi 10.1002/nla.2497 doi 11420/15087 hdl (DE-627)1841110280 (DE-599)KXP1841110280 DE-627 ger DE-627 rda eng 510: Mathematik Le Borne, Sabine verfasserin (DE-588)1162159316 (DE-627)1025603109 (DE-576)507230957 aut A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. DE-830 Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International CC BY-NC-ND 4.0 cc https://creativecommons.org/licenses/by-nc-nd/4.0/ block QR factorization DSpace Householder method DSpace Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Numerical linear algebra with applications New York, NY [u.a.] : Wiley, 1994 00(2023), 0, Seite 1-10 Online-Ressource (DE-627)318472139 (DE-600)2012602-5 (DE-576)11461766X 1099-1506 nnns volume:00 year:2023 number:0 pages:1-10 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215239 Resolving-System kostenfrei https://doi.org/10.15480/882.5036 Resolving-System kostenfrei http://hdl.handle.net/11420/15087 Resolving-System kostenfrei https://doi.org/10.1002/nla.2497 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 0 1-10 045F 510: Mathematik 23 01 0830 4301528644 Opus Elektronischer Volltext f z 04-04-23 23 01 0830 https://doi.org/10.15480/882.5036 LF 23 01 0830 Opus 23 01 0830 tubdok 23 01 0830 tuhh |
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urn:nbn:de:gbv:830-882.0215239 urn 10.15480/882.5036 doi 10.1002/nla.2497 doi 11420/15087 hdl (DE-627)1841110280 (DE-599)KXP1841110280 DE-627 ger DE-627 rda eng 510: Mathematik Le Borne, Sabine verfasserin (DE-588)1162159316 (DE-627)1025603109 (DE-576)507230957 aut A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. DE-830 Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International CC BY-NC-ND 4.0 cc https://creativecommons.org/licenses/by-nc-nd/4.0/ block QR factorization DSpace Householder method DSpace Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Numerical linear algebra with applications New York, NY [u.a.] : Wiley, 1994 00(2023), 0, Seite 1-10 Online-Ressource (DE-627)318472139 (DE-600)2012602-5 (DE-576)11461766X 1099-1506 nnns volume:00 year:2023 number:0 pages:1-10 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215239 Resolving-System kostenfrei https://doi.org/10.15480/882.5036 Resolving-System kostenfrei http://hdl.handle.net/11420/15087 Resolving-System kostenfrei https://doi.org/10.1002/nla.2497 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 0 1-10 045F 510: Mathematik 23 01 0830 4301528644 Opus Elektronischer Volltext f z 04-04-23 23 01 0830 https://doi.org/10.15480/882.5036 LF 23 01 0830 Opus 23 01 0830 tubdok 23 01 0830 tuhh |
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Le Borne, Sabine |
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Le Borne, Sabine ddc 510: Mathematik DSpace block QR factorization DSpace Householder method A block Cholesky-LU-based QR factorization for rectangular matrices |
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510: Mathematik A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne block QR factorization DSpace Householder method DSpace |
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A block Cholesky-LU-based QR factorization for rectangular matrices |
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A block Cholesky-LU-based QR factorization for rectangular matrices Sabine Le Borne |
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block cholesky-lu-based qr factorization for rectangular matrices |
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A block Cholesky-LU-based QR factorization for rectangular matrices |
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The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik |
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The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik |
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The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods. Sonstige Körperschaften: Technische Universität Hamburg Sonstige Körperschaften: Technische Universität Hamburg, Institut für Mathematik |
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A block Cholesky-LU-based QR factorization for rectangular matrices |
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| score |
7.4001036 |