When a maximal angle among cones is nonobtuse
Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Orlitzky, Michael [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Computational and applied mathematics - Berlin : Springer, 2003, 39(2020), 2 vom: 19. Feb. |
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| Übergeordnetes Werk: |
volume:39 ; year:2020 ; number:2 ; day:19 ; month:02 |
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| DOI / URN: |
10.1007/s40314-020-1115-y |
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| Katalog-ID: |
SPR036819565 |
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| 245 | 1 | 0 | |a When a maximal angle among cones is nonobtuse |
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| 520 | |a Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. | ||
| 650 | 4 | |a Critical angle |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Maximal angle |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Nash angle |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Convex cone |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Polyhedral cone |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Principal angle |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Nonconvex optimization |7 (dpeaa)DE-He213 | |
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10.1007/s40314-020-1115-y doi (DE-627)SPR036819565 (SPR)s40314-020-1115-y-e DE-627 ger DE-627 rakwb eng Orlitzky, Michael verfasserin (orcid)0000-0002-1447-961X aut When a maximal angle among cones is nonobtuse 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 19. Feb. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:19 month:02 https://dx.doi.org/10.1007/s40314-020-1115-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 AR 39 2020 2 19 02 |
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10.1007/s40314-020-1115-y doi (DE-627)SPR036819565 (SPR)s40314-020-1115-y-e DE-627 ger DE-627 rakwb eng Orlitzky, Michael verfasserin (orcid)0000-0002-1447-961X aut When a maximal angle among cones is nonobtuse 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 19. Feb. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:19 month:02 https://dx.doi.org/10.1007/s40314-020-1115-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 AR 39 2020 2 19 02 |
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10.1007/s40314-020-1115-y doi (DE-627)SPR036819565 (SPR)s40314-020-1115-y-e DE-627 ger DE-627 rakwb eng Orlitzky, Michael verfasserin (orcid)0000-0002-1447-961X aut When a maximal angle among cones is nonobtuse 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 19. Feb. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:19 month:02 https://dx.doi.org/10.1007/s40314-020-1115-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 AR 39 2020 2 19 02 |
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10.1007/s40314-020-1115-y doi (DE-627)SPR036819565 (SPR)s40314-020-1115-y-e DE-627 ger DE-627 rakwb eng Orlitzky, Michael verfasserin (orcid)0000-0002-1447-961X aut When a maximal angle among cones is nonobtuse 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 19. Feb. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:19 month:02 https://dx.doi.org/10.1007/s40314-020-1115-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 AR 39 2020 2 19 02 |
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10.1007/s40314-020-1115-y doi (DE-627)SPR036819565 (SPR)s40314-020-1115-y-e DE-627 ger DE-627 rakwb eng Orlitzky, Michael verfasserin (orcid)0000-0002-1447-961X aut When a maximal angle among cones is nonobtuse 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 19. Feb. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:19 month:02 https://dx.doi.org/10.1007/s40314-020-1115-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 AR 39 2020 2 19 02 |
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Orlitzky, Michael |
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Orlitzky, Michael misc Critical angle misc Maximal angle misc Nash angle misc Convex cone misc Polyhedral cone misc Principal angle misc Nonconvex optimization When a maximal angle among cones is nonobtuse |
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When a maximal angle among cones is nonobtuse Critical angle (dpeaa)DE-He213 Maximal angle (dpeaa)DE-He213 Nash angle (dpeaa)DE-He213 Convex cone (dpeaa)DE-He213 Polyhedral cone (dpeaa)DE-He213 Principal angle (dpeaa)DE-He213 Nonconvex optimization (dpeaa)DE-He213 |
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When a maximal angle among cones is nonobtuse |
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when a maximal angle among cones is nonobtuse |
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When a maximal angle among cones is nonobtuse |
| abstract |
Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 |
| abstractGer |
Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 |
| abstract_unstemmed |
Abstract Principal angles between linear subspaces have been studied for their application to statistics, numerical linear algebra, and other areas. In 2005, Iusem and Seeger defined critical angles within a single convex cone as an extension of antipodality in a compact set. Then, in 2016, Seeger and Sossa extended that notion to two cones. This was motivated in part by an application to regression analysis, but also allows their cone theory to encompass linear subspaces which are themselves convex cones. One obstacle to computing the maximal critical angle between cones is that, in general, the maximum will not occur at a pair of generators of the cones. We show that in the special case where the maximal angle between the cones is nonobtuse, it does suffice to check only the generators. This special case can be checked at essentially no extra cost, and we incorporate that information into an improved algorithm to find the maximal angle. © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020 |
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When a maximal angle among cones is nonobtuse |
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https://dx.doi.org/10.1007/s40314-020-1115-y |
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10.1007/s40314-020-1115-y |
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2024-07-03T19:45:01.617Z |
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