Computing eigenvalues of normal matrices via complex symmetric matrices

Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this in...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ferranti, Micol [verfasserIn] Vandebril, Raf [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition

Übergeordnetes Werk:	Enthalten in: Journal of computational and applied mathematics - Amsterdam [u.a.] : North-Holland, 1975, 259, Seite 281-293
Übergeordnetes Werk:	volume:259 ; pages:281-293

DOI / URN:	10.1016/j.cam.2013.08.036

Katalog-ID:	ELV002620340

Internformat


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024	7		\|a 10.1016/j.cam.2013.08.036 \|2 doi
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100	1		\|a Ferranti, Micol \|e verfasserin \|4 aut
245	1	0	\|a Computing eigenvalues of normal matrices via complex symmetric matrices
264		1	\|c 2013
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix.
650		4	\|a Normal matrix
650		4	\|a Complex symmetric
650		4	\|a Takagi factorization
650		4	\|a Unitary similarity
650		4	\|a Symmetric singular value decomposition
650		4	\|a Eigenvalue decomposition
700	1		\|a Vandebril, Raf \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of computational and applied mathematics \|d Amsterdam [u.a.] : North-Holland, 1975 \|g 259, Seite 281-293 \|h Online-Ressource \|w (DE-627)266889204 \|w (DE-600)1468806-2 \|w (DE-576)075962373 \|7 nnns
773	1	8	\|g volume:259 \|g pages:281-293
912			\|a GBV_USEFLAG_U
912			\|a SYSFLAG_U
912			\|a GBV_ELV
912			\|a SSG-OPC-MAT
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4392
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.00 \|j Mathematik: Allgemeines
951			\|a AR
952			\|d 259 \|h 281-293

Indexfelder

author_variant	m f mf r v rv
matchkey_str	ferrantimicolvandebrilraf:2013----:optnegnausfomlarcsicml
hierarchy_sort_str	2013
bklnumber	31.00
publishDate	2013
allfields	10.1016/j.cam.2013.08.036 doi (DE-627)ELV002620340 (ELSEVIER)S0377-0427(13)00450-0 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Ferranti, Micol verfasserin aut Computing eigenvalues of normal matrices via complex symmetric matrices 2013 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix. Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition Vandebril, Raf verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 259, Seite 281-293 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:259 pages:281-293 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 259 281-293
spelling	10.1016/j.cam.2013.08.036 doi (DE-627)ELV002620340 (ELSEVIER)S0377-0427(13)00450-0 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Ferranti, Micol verfasserin aut Computing eigenvalues of normal matrices via complex symmetric matrices 2013 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix. Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition Vandebril, Raf verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 259, Seite 281-293 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:259 pages:281-293 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 259 281-293
allfields_unstemmed	10.1016/j.cam.2013.08.036 doi (DE-627)ELV002620340 (ELSEVIER)S0377-0427(13)00450-0 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Ferranti, Micol verfasserin aut Computing eigenvalues of normal matrices via complex symmetric matrices 2013 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix. Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition Vandebril, Raf verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 259, Seite 281-293 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:259 pages:281-293 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 259 281-293
allfieldsGer	10.1016/j.cam.2013.08.036 doi (DE-627)ELV002620340 (ELSEVIER)S0377-0427(13)00450-0 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Ferranti, Micol verfasserin aut Computing eigenvalues of normal matrices via complex symmetric matrices 2013 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix. Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition Vandebril, Raf verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 259, Seite 281-293 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:259 pages:281-293 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 259 281-293
allfieldsSound	10.1016/j.cam.2013.08.036 doi (DE-627)ELV002620340 (ELSEVIER)S0377-0427(13)00450-0 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Ferranti, Micol verfasserin aut Computing eigenvalues of normal matrices via complex symmetric matrices 2013 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix. Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition Vandebril, Raf verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 259, Seite 281-293 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:259 pages:281-293 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 259 281-293
language	English
source	Enthalten in Journal of computational and applied mathematics 259, Seite 281-293 volume:259 pages:281-293
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topic_facet	Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition
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author	Ferranti, Micol
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topic_title	510 DE-600 31.00 bkl Computing eigenvalues of normal matrices via complex symmetric matrices Normal matrix Complex symmetric Takagi factorization Unitary similarity Symmetric singular value decomposition Eigenvalue decomposition
topic	ddc 510 bkl 31.00 misc Normal matrix misc Complex symmetric misc Takagi factorization misc Unitary similarity misc Symmetric singular value decomposition misc Eigenvalue decomposition
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title	Computing eigenvalues of normal matrices via complex symmetric matrices
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title_full	Computing eigenvalues of normal matrices via complex symmetric matrices
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title_sort	computing eigenvalues of normal matrices via complex symmetric matrices
title_auth	Computing eigenvalues of normal matrices via complex symmetric matrices
abstract	Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix.
abstractGer	Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix.
abstract_unstemmed	Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. Unfortunately, such a condensed format does not exist for a generic normal matrix.
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title_short	Computing eigenvalues of normal matrices via complex symmetric matrices
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up_date	2024-07-06T16:53:11.383Z
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In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues of this condensed matrix are computed. The main purpose of this intermediate matrix is saving valuable computing time. Important subclasses of normal matrices, such as the Hermitian, skew-Hermitian and unitary matrices admit a condensed matrix represented by only O ( n ) parameters, allowing subsequent low-cost algorithms to compute their eigenvalues. 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Computing eigenvalues of normal matrices via complex symmetric matrices

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