Spectral properties of flipped Toeplitz matrices and related preconditioning

Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange mat...
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Gespeichert in:

Autor*in:	Mazza, M. [verfasserIn] Pestana, J. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Toeplitz matrices Spectral symbol GLT theory Hankel matrices

Übergeordnetes Werk:	Enthalten in: BIT - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961, 59(2018), 2 vom: 18. Dez., Seite 463-482
Übergeordnetes Werk:	volume:59 ; year:2018 ; number:2 ; day:18 ; month:12 ; pages:463-482

Links:	Volltext

DOI / URN:	10.1007/s10543-018-0740-y

Katalog-ID:	SPR011133910

Internformat


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245	1	0	\|a Spectral properties of flipped Toeplitz matrices and related preconditioning
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520			\|a Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings.
650		4	\|a Toeplitz matrices \|7 (dpeaa)DE-He213
650		4	\|a Spectral symbol \|7 (dpeaa)DE-He213
650		4	\|a GLT theory \|7 (dpeaa)DE-He213
650		4	\|a Hankel matrices \|7 (dpeaa)DE-He213
700	1		\|a Pestana, J. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t BIT \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 \|g 59(2018), 2 vom: 18. Dez., Seite 463-482 \|w (DE-627)265778360 \|w (DE-600)1465706-5 \|x 1572-9125 \|7 nnns
773	1	8	\|g volume:59 \|g year:2018 \|g number:2 \|g day:18 \|g month:12 \|g pages:463-482
856	4	0	\|u https://dx.doi.org/10.1007/s10543-018-0740-y \|z kostenfrei \|3 Volltext
912			\|a GBV_USEFLAG_A
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912			\|a GBV_SPRINGER
912			\|a SSG-OPC-BBI
912			\|a SSG-OPC-MAT
912			\|a SSG-OPC-ASE
912			\|a GBV_ILN_11
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_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_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
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_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
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_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
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_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.76 \|q ASE
951			\|a AR
952			\|d 59 \|j 2018 \|e 2 \|b 18 \|c 12 \|h 463-482

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author_variant	m m mm j p jp
matchkey_str	article:15729125:2018----::pcrlrprisflpeteltmtieadea
hierarchy_sort_str	2018
bklnumber	31.76
publishDate	2018
allfields	10.1007/s10543-018-0740-y doi (DE-627)SPR011133910 (SPR)s10543-018-0740-y-e DE-627 ger DE-627 rakwb eng 070 ASE 31.76 bkl Mazza, M. verfasserin aut Spectral properties of flipped Toeplitz matrices and related preconditioning 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings. Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213 Pestana, J. verfasserin aut Enthalten in BIT Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 59(2018), 2 vom: 18. Dez., Seite 463-482 (DE-627)265778360 (DE-600)1465706-5 1572-9125 nnns volume:59 year:2018 number:2 day:18 month:12 pages:463-482 https://dx.doi.org/10.1007/s10543-018-0740-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 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_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 59 2018 2 18 12 463-482
spelling	10.1007/s10543-018-0740-y doi (DE-627)SPR011133910 (SPR)s10543-018-0740-y-e DE-627 ger DE-627 rakwb eng 070 ASE 31.76 bkl Mazza, M. verfasserin aut Spectral properties of flipped Toeplitz matrices and related preconditioning 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings. Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213 Pestana, J. verfasserin aut Enthalten in BIT Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 59(2018), 2 vom: 18. Dez., Seite 463-482 (DE-627)265778360 (DE-600)1465706-5 1572-9125 nnns volume:59 year:2018 number:2 day:18 month:12 pages:463-482 https://dx.doi.org/10.1007/s10543-018-0740-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 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_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 59 2018 2 18 12 463-482
allfields_unstemmed	10.1007/s10543-018-0740-y doi (DE-627)SPR011133910 (SPR)s10543-018-0740-y-e DE-627 ger DE-627 rakwb eng 070 ASE 31.76 bkl Mazza, M. verfasserin aut Spectral properties of flipped Toeplitz matrices and related preconditioning 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings. Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213 Pestana, J. verfasserin aut Enthalten in BIT Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 59(2018), 2 vom: 18. Dez., Seite 463-482 (DE-627)265778360 (DE-600)1465706-5 1572-9125 nnns volume:59 year:2018 number:2 day:18 month:12 pages:463-482 https://dx.doi.org/10.1007/s10543-018-0740-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 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_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 59 2018 2 18 12 463-482
allfieldsGer	10.1007/s10543-018-0740-y doi (DE-627)SPR011133910 (SPR)s10543-018-0740-y-e DE-627 ger DE-627 rakwb eng 070 ASE 31.76 bkl Mazza, M. verfasserin aut Spectral properties of flipped Toeplitz matrices and related preconditioning 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings. Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213 Pestana, J. verfasserin aut Enthalten in BIT Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 59(2018), 2 vom: 18. Dez., Seite 463-482 (DE-627)265778360 (DE-600)1465706-5 1572-9125 nnns volume:59 year:2018 number:2 day:18 month:12 pages:463-482 https://dx.doi.org/10.1007/s10543-018-0740-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 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_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 59 2018 2 18 12 463-482
allfieldsSound	10.1007/s10543-018-0740-y doi (DE-627)SPR011133910 (SPR)s10543-018-0740-y-e DE-627 ger DE-627 rakwb eng 070 ASE 31.76 bkl Mazza, M. verfasserin aut Spectral properties of flipped Toeplitz matrices and related preconditioning 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings. Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213 Pestana, J. verfasserin aut Enthalten in BIT Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961 59(2018), 2 vom: 18. Dez., Seite 463-482 (DE-627)265778360 (DE-600)1465706-5 1572-9125 nnns volume:59 year:2018 number:2 day:18 month:12 pages:463-482 https://dx.doi.org/10.1007/s10543-018-0740-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 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_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 59 2018 2 18 12 463-482
language	English
source	Enthalten in BIT 59(2018), 2 vom: 18. Dez., Seite 463-482 volume:59 year:2018 number:2 day:18 month:12 pages:463-482
sourceStr	Enthalten in BIT 59(2018), 2 vom: 18. Dez., Seite 463-482 volume:59 year:2018 number:2 day:18 month:12 pages:463-482
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Toeplitz matrices Spectral symbol GLT theory Hankel matrices
dewey-raw	070
isfreeaccess_bool	true
container_title	BIT
authorswithroles_txt_mv	Mazza, M. @@aut@@ Pestana, J. @@aut@@
publishDateDaySort_date	2018-12-18T00:00:00Z
hierarchy_top_id	265778360
dewey-sort	270
id	SPR011133910
language_de	englisch
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author	Mazza, M.
spellingShingle	Mazza, M. ddc 070 bkl 31.76 misc Toeplitz matrices misc Spectral symbol misc GLT theory misc Hankel matrices Spectral properties of flipped Toeplitz matrices and related preconditioning
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topic_title	070 ASE 31.76 bkl Spectral properties of flipped Toeplitz matrices and related preconditioning Toeplitz matrices (dpeaa)DE-He213 Spectral symbol (dpeaa)DE-He213 GLT theory (dpeaa)DE-He213 Hankel matrices (dpeaa)DE-He213
topic	ddc 070 bkl 31.76 misc Toeplitz matrices misc Spectral symbol misc GLT theory misc Hankel matrices
topic_unstemmed	ddc 070 bkl 31.76 misc Toeplitz matrices misc Spectral symbol misc GLT theory misc Hankel matrices
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title	Spectral properties of flipped Toeplitz matrices and related preconditioning
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title_full	Spectral properties of flipped Toeplitz matrices and related preconditioning
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title_sort	spectral properties of flipped toeplitz matrices and related preconditioning
title_auth	Spectral properties of flipped Toeplitz matrices and related preconditioning
abstract	Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings.
abstractGer	Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings.
abstract_unstemmed	Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings.
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title_short	Spectral properties of flipped Toeplitz matrices and related preconditioning
url	https://dx.doi.org/10.1007/s10543-018-0740-y
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author2	Pestana, J.
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doi_str	10.1007/s10543-018-0740-y
up_date	2024-07-03T20:41:03.483Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR011133910</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110223448.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2018 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10543-018-0740-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR011133910</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10543-018-0740-y-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">070</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mazza, M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Spectral properties of flipped Toeplitz matrices and related preconditioning</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this work, we investigate the spectra of “flipped” Toeplitz sequences, i.e., the asymptotic spectral behaviour of %$\{Y_nT_n(f)\}_n%$, where %$T_n(f)\in \mathbb {R}^{n\times n}%$ is a real Toeplitz matrix generated by a function %$f\in L^1([-\pi ,\pi ])%$, and %$Y_n%$ is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of %$Y_nT_n(f)%$ are asymptotically described by a %$2\times 2%$ matrix-valued function, whose eigenvalue functions are %$\pm \, \|f\|%$. It turns out that roughly half of the eigenvalues of %$Y_nT_n(f)%$ are well approximated by a uniform sampling of \|f\| over %$[-\,\pi ,\pi ]%$, while the remaining are well approximated by a uniform sampling of %$-\,\|f\|%$ over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Toeplitz matrices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spectral symbol</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">GLT theory</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hankel matrices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pestana, J.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">BIT</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961</subfield><subfield code="g">59(2018), 2 vom: 18. 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