Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme
Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-(R1, R2, R3) approximation of third-order t...
Uloženo v:
| Vydáno v: | SIAM journal on matrix analysis and applications Ročník 32; číslo 1; s. 115 - 135 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.01.2011
|
| Témata: | |
| ISSN: | 0895-4798, 1095-7162 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-(R1, R2, R3) approximation of third-order tensors. We propose a new iterative algorithm based on the trust-region scheme. The tensor approximation problem is expressed as a minimization of a cost function on a product of three Grassmann manifolds. We apply the Riemannian trust-region scheme, using the truncated conjugate-gradient method for solving the trust-region subproblem. Making use of second order information of the cost function, superlinear convergence is achieved. If the stopping criterion of the subproblem is chosen adequately, the local convergence rate is quadratic. We compare this new method with the well-known higher-order orthogonal iteration method and discuss the advantages over Newton-type methods. [PUBLICATION ABSTRACT] |
|---|---|
| AbstractList | Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-(R1, R2, R3) approximation of third-order tensors. We propose a new iterative algorithm based on the trust-region scheme. The tensor approximation problem is expressed as a minimization of a cost function on a product of three Grassmann manifolds. We apply the Riemannian trust-region scheme, using the truncated conjugate-gradient method for solving the trust-region subproblem. Making use of second order information of the cost function, superlinear convergence is achieved. If the stopping criterion of the subproblem is chosen adequately, the local convergence rate is quadratic. We compare this new method with the well-known higher-order orthogonal iteration method and discuss the advantages over Newton-type methods. [PUBLICATION ABSTRACT] Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-(R1, R2, R3) approximation of third-order tensors. We propose a new iterative algorithm based on the trust-region scheme. The tensor approximation problem is expressed as a minimization of a cost function on a product of three Grassmann manifolds. We apply the Riemannian trust-region scheme, using the truncated conjugate-gradient method for solving the trust-region subproblem. Making use of second order information of the cost function, superlinear convergence is achieved. If the stopping criterion of the subproblem is chosen adequately, the local convergence rate is quadratic. We compare this new method with the well-known higher-order orthogonal iteration method and discuss the advantages over Newton-type methods. |
| Author | Ishteva, Mariya Absil, P.-A. De Lathauwer, Lieven Van Huffel, Sabine |
| Author_xml | – sequence: 1 givenname: Mariya surname: Ishteva fullname: Ishteva, Mariya – sequence: 2 givenname: P.-A. surname: Absil fullname: Absil, P.-A. – sequence: 3 givenname: Sabine surname: Van Huffel fullname: Van Huffel, Sabine – sequence: 4 givenname: Lieven surname: De Lathauwer fullname: De Lathauwer, Lieven |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24190950$$DView record in Pascal Francis |
| BookMark | eNplkUFPGzEQhS0EUgP0wD-wkJBA6hJ7vbu2j4DaUikIKQ1ny-sdJw4bO9i7gv77mkI5hNPM4XtPM-8don0fPCB0QsklpYxPiSS8qUTJ99CEElkXnDblPpoQkfeKS_EFHaa0JoQ2laQT1F9DGvAsPOO7sR9c7zzoiOfaP-Kr7TaGF7fRgwseB4tv3XIFsbiPHUS8AJ9CTN_wtU7Q4UwMK8BzBxvtvdMeL-KYhmIOy1f1b7OCDRyjA6v7BF_f5xF6-PF9cXNbzO5__rq5mhWGiXoomLQUODPayqptKGGmAdER3rEKylLXreY1SGqFqGTLiLEVQNsBIcK0whDLjtD5m29-4GnMD6qNSwb6XnsIY1K04ZRRWrM6o6c76DqM0efrlOCSl2WOMkNn75BORvc2am9cUtuYw4l_VFlRmaMmmZu-cSaGlCJYZdzwL74hatcrStRrSeqjpKy42FH8N_3M_gXms5JA |
| CODEN | SJMAEL |
| CitedBy_id | crossref_primary_10_1007_s00211_012_0464_x crossref_primary_10_1145_2532169 crossref_primary_10_1007_s11075_022_01303_0 crossref_primary_10_1002_gamm_201310004 crossref_primary_10_1109_TBME_2018_2847404 crossref_primary_10_1090_mcom_3834 crossref_primary_10_1109_ACCESS_2023_3326073 crossref_primary_10_1190_geo2014_0594_1 crossref_primary_10_1109_TSP_2017_2690524 crossref_primary_10_1137_140956865 crossref_primary_10_1080_03081087_2017_1391743 crossref_primary_10_1016_j_neucom_2017_04_058 crossref_primary_10_1007_s10915_021_01545_5 crossref_primary_10_1007_s10444_025_10232_0 crossref_primary_10_1080_03081087_2016_1234578 crossref_primary_10_1016_j_apnum_2024_03_004 crossref_primary_10_1109_LCOMM_2012_040912_120298 crossref_primary_10_1016_j_image_2017_10_001 crossref_primary_10_1137_21M1463896 crossref_primary_10_1007_s11075_025_02136_3 crossref_primary_10_1016_j_neucom_2025_130330 crossref_primary_10_1007_s10589_020_00167_1 crossref_primary_10_1007_s10957_019_01539_2 crossref_primary_10_1016_j_cam_2020_113380 crossref_primary_10_1002_nla_2175 crossref_primary_10_1109_TSP_2017_2703882 crossref_primary_10_1137_17M114618X crossref_primary_10_1137_12088906X crossref_primary_10_1016_j_cam_2019_03_002 crossref_primary_10_1109_TSP_2016_2620965 crossref_primary_10_1007_s10543_025_01066_9 crossref_primary_10_1007_s10898_024_01378_0 crossref_primary_10_1137_100792032 crossref_primary_10_1109_TKDE_2012_95 crossref_primary_10_1137_110830034 crossref_primary_10_1137_23M1582928 crossref_primary_10_1137_23M1594066 crossref_primary_10_1007_s10479_025_06614_8 crossref_primary_10_1137_15M1037288 crossref_primary_10_1109_OJSP_2025_3607278 crossref_primary_10_1007_s42514_019_00012_w crossref_primary_10_1109_ACCESS_2021_3058103 crossref_primary_10_1137_130943133 crossref_primary_10_1002_nla_2363 crossref_primary_10_1137_23M1622830 crossref_primary_10_1002_nla_2202 crossref_primary_10_1137_16M1069298 crossref_primary_10_1007_s10915_021_01493_0 crossref_primary_10_1109_MSP_2013_2297439 crossref_primary_10_1007_s11075_024_01921_w crossref_primary_10_1016_j_apnum_2022_08_005 crossref_primary_10_1109_MSP_2020_3003544 crossref_primary_10_3390_a16020117 crossref_primary_10_1137_11085743X crossref_primary_10_1007_s10440_020_00332_y crossref_primary_10_1007_s40314_020_01328_y crossref_primary_10_1137_19M1257147 crossref_primary_10_1137_19M1237016 crossref_primary_10_1080_03081087_2016_1164660 crossref_primary_10_1137_110836067 crossref_primary_10_1137_17M1152371 crossref_primary_10_1007_s40305_023_00462_8 crossref_primary_10_1137_18M1168285 crossref_primary_10_1007_s10444_018_9622_8 crossref_primary_10_1007_s40314_020_1124_x crossref_primary_10_1137_17M112213X crossref_primary_10_1007_s10107_014_0765_1 crossref_primary_10_1007_s10898_022_01182_8 crossref_primary_10_1007_s11336_017_9568_7 |
| Cites_doi | 10.1016/0165-1684(94)90029-9 10.1155/2007/58253 10.1016/j.neuroimage.2007.04.041 10.1137/07070111X 10.1109/78.824675 10.1093/bioinformatics/btm210 10.1002/sapm192761164 10.1007/s10208-005-0179-9 10.1007/BF02293599 10.1073/pnas.112329799 10.1137/060657017 10.1137/070688316 10.1007/s11075-008-9251-2 10.1137/0720042 10.1016/j.sigpro.2005.12.015 10.1137/060655936 10.1137/S0895479898346995 10.1137/060655894 10.1162/neco.2008.04-08-749 10.1002/1099-128X(200005/06)14:3<123::AID-CEM589>3.0.CO;2-1 10.1002/sapm19287139 10.1109/78.852018 10.1137/090763172 10.1137/040604959 10.1016/S0165-1684(97)00065-0 10.1002/cem.1212 10.1109/TSP.2008.917929 10.1016/j.neuroimage.2005.08.005 10.1002/nla.453 10.1007/BF02289464 10.1137/S0895479896305696 10.1137/0904038 10.1016/j.laa.2004.01.016 10.1109/79.221324 |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS Copyright Society for Industrial and Applied Mathematics 2011 |
| Copyright_xml | – notice: 2015 INIST-CNRS – notice: Copyright Society for Industrial and Applied Mathematics 2011 |
| DBID | AAYXX CITATION IQODW 3V. 7WY 7WZ 7X2 7XB 87Z 88A 88F 88I 88K 8AL 8FE 8FG 8FH 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI CCPQU D1I DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- KB. L.- L6V LK8 M0C M0K M0N M1Q M2O M2P M2T M7P M7S MBDVC P5Z P62 PATMY PDBOC PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYCSY Q9U 7SC 8FD L7M L~C L~D |
| DOI | 10.1137/090764827 |
| DatabaseName | CrossRef Pascal-Francis ProQuest Central (Corporate) ABI/INFORM Collection ABI/INFORM Global (PDF only) Agricultural Science Collection ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Biology Database (Alumni Edition) Military Database (Alumni Edition) Science Database (Alumni Edition) Telecommunications (Alumni Edition) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Research Library (Alumni) ProQuest SciTech Premium Collection Technology Collection Materials Science & Engineering Database ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest SciTech Premium Collection Technology Collection Advanced Technologies & Aerospace Collection Agricultural & Environmental Science Collection ProQuest Central Essentials - QC ProQuest SciTech Premium Collection Natural Science Collection Biological Science Collection ProQuest Central Business Premium Collection Technology Collection (via ProQuest SciTech Premium Collection) Natural Science Collection ProQuest One ProQuest Materials Science Collection ProQuest Central Korea Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student Research Library Prep SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database Materials Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection Biological Sciences ABI/INFORM Global Agriculture Science Database Computing Database Military Database (ProQuest) Research Library (ProQuest) Science Database Telecommunications Database Biological Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Environmental Science Database Materials Science Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection Environmental Science Collection ProQuest Central Basic Computer and Information Systems Abstracts Technology Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Agricultural Science Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest Military Collection ProQuest Central China ABI/INFORM Complete ProQuest Telecommunications ProQuest One Applied & Life Sciences Natural Science Collection Biological Science Collection ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Technology Collection ProQuest Telecommunications (Alumni Edition) Biological Science Database ProQuest Business Collection Environmental Science Collection ProQuest One Academic UKI Edition Environmental Science Database ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection ProQuest One Academic Middle East (New) Materials Science Collection ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Natural Science Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea Agricultural & Environmental Science Collection Materials Science Database ProQuest Research Library ABI/INFORM Complete (Alumni Edition) ProQuest Materials Science Collection ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest Military Collection (Alumni Edition) ProQuest SciTech Collection Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Agricultural Science Database Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Statistics |
| EISSN | 1095-7162 |
| EndPage | 135 |
| ExternalDocumentID | 2410778121 24190950 10_1137_090764827 |
| Genre | Feature |
| GroupedDBID | -~X .4S .DC 123 186 4.4 7WY 7X2 7XC 88I 8CJ 8FE 8FG 8FH 8FL 8G5 8V8 AALVN AASXH AAYXX ABDBF ABDPE ABJCF ABKAD ABMZU ABUWG ACGFO ACGOD ACIWK ACPRK ACUHS ADBBV AEMOZ AENEX AFFHD AFFNX AFKRA AFRAH AHQJS AKVCP ALMA_UNASSIGNED_HOLDINGS ANXRF ARAPS ARCSS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI BPHCQ CCPQU CITATION CS3 CZ9 D0L D1I D1J D1K DQ2 DU5 DWQXO EAP EBR EBS EBU ECS EDO EJD EMK EST ESX FA8 FRNLG GNUQQ GUQSH H13 HCIFZ H~9 I-F K1G K6- K60 K6V K6~ K7- KB. KC. L6V LK5 LK8 M0C M0K M1Q M2O M2P M7P M7R M7S P1Q P2P P62 PATMY PDBOC PHGZM PHGZT PQBIZ PQBZA PQGLB PQQKQ PROAC PTHSS PYCSY RJG RNS RSI TH9 TN5 TUS YNT ZKB ZY4 IQODW 3V. 7XB 88A 88K 8AL 8FK JQ2 L.- M0N M2T MBDVC PKEHL PQEST PQUKI PRINS Q9U 7SC 8FD L7M L~C L~D PUEGO |
| ID | FETCH-LOGICAL-c385t-39f1e73caf94b6103c6e8d07d34e22a5ba75e91f8849b30cf4eebde008cb8c0f3 |
| IEDL.DBID | M1Q |
| ISICitedReferencesCount | 95 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000292816300006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0895-4798 |
| IngestDate | Thu Oct 02 10:57:33 EDT 2025 Fri Jul 25 12:28:42 EDT 2025 Mon Jul 21 09:15:34 EDT 2025 Tue Nov 18 21:35:33 EST 2025 Sat Nov 29 02:43:41 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Cost minimization Second order Product Iteration multilinear algebra Riemann manifold Grassmann manifold Three manifold 65F99 Approximation order Convergence rate Cost function Singular value decomposition Conjugate gradient method 53B20 Approximation Tensor Solving Rank 90C48 15A69 Riemannian manifold Statistics rank reduction Statistical method Array Numerical analysis Scientific computation Function minimization Linear algebra Signal processing Best approximation trust-region scheme 49M37 higher-order tensor |
| Language | English |
| License | CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c385t-39f1e73caf94b6103c6e8d07d34e22a5ba75e91f8849b30cf4eebde008cb8c0f3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| PQID | 879722827 |
| PQPubID | 666305 |
| PageCount | 21 |
| ParticipantIDs | proquest_miscellaneous_1671311535 proquest_journals_879722827 pascalfrancis_primary_24190950 crossref_citationtrail_10_1137_090764827 crossref_primary_10_1137_090764827 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-01-00 2011 20110101 |
| PublicationDateYYYYMMDD | 2011-01-01 |
| PublicationDate_xml | – month: 01 year: 2011 text: 2011-01-00 |
| PublicationDecade | 2010 |
| PublicationPlace | Philadelphia, PA |
| PublicationPlace_xml | – name: Philadelphia, PA – name: Philadelphia |
| PublicationTitle | SIAM journal on matrix analysis and applications |
| PublicationYear | 2011 |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher_xml | – name: Society for Industrial and Applied Mathematics |
| References | R41 R40 R21 R43 R20 R22 R44 R25 R47 R26 R28 R1 R2 Ishteva M. (R24) 2008; 42 R4 R5 R6 R7 R8 R30 R10 R32 R31 R12 R11 R14 R36 R13 R35 R16 R15 R37 R17 R39 R19 |
| References_xml | – ident: R8 doi: 10.1016/0165-1684(94)90029-9 – ident: R15 doi: 10.1155/2007/58253 – ident: R16 doi: 10.1016/j.neuroimage.2007.04.041 – ident: R26 doi: 10.1137/07070111X – ident: R41 doi: 10.1109/78.824675 – ident: R4 doi: 10.1093/bioinformatics/btm210 – ident: R21 doi: 10.1002/sapm192761164 – ident: R1 doi: 10.1007/s10208-005-0179-9 – ident: R28 doi: 10.1007/BF02293599 – ident: R6 doi: 10.1073/pnas.112329799 – ident: R20 doi: 10.1137/060657017 – ident: R17 doi: 10.1137/070688316 – ident: R25 doi: 10.1007/s11075-008-9251-2 – ident: R43 doi: 10.1137/0720042 – ident: R10 doi: 10.1016/j.sigpro.2005.12.015 – ident: R5 doi: 10.1137/060655936 – ident: R13 doi: 10.1137/S0895479898346995 – ident: R35 doi: 10.1137/060655894 – ident: R2 doi: 10.1162/neco.2008.04-08-749 – ident: R11 doi: 10.1002/1099-128X(200005/06)14:3<123::AID-CEM589>3.0.CO;2-1 – ident: R22 doi: 10.1002/sapm19287139 – volume: 42 start-page: 337 year: 2008 ident: R24 publication-title: Int. J. Pure Appl. Math. – ident: R40 doi: 10.1109/78.852018 – ident: R39 doi: 10.1137/090763172 – ident: R7 doi: 10.1137/040604959 – ident: R44 doi: 10.1016/S0165-1684(97)00065-0 – ident: R37 doi: 10.1002/cem.1212 – ident: R19 doi: 10.1109/TSP.2008.917929 – ident: R31 doi: 10.1016/j.neuroimage.2005.08.005 – ident: R36 doi: 10.1002/nla.453 – ident: R47 doi: 10.1007/BF02289464 – ident: R12 doi: 10.1137/S0895479896305696 – ident: R30 doi: 10.1137/0904038 – ident: R14 doi: 10.1016/j.laa.2004.01.016 – ident: R32 doi: 10.1109/79.221324 |
| SSID | ssj0016491 |
| Score | 2.3057587 |
| Snippet | Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms... |
| SourceID | proquest pascalfrancis crossref |
| SourceType | Aggregation Database Index Database Enrichment Source |
| StartPage | 115 |
| SubjectTerms | Algebra Algebraic geometry Algorithms Approximation Arrays Convergence Cost function Exact sciences and technology Geometry Iterative methods Linear algebra Linear and multilinear algebra, matrix theory Manifolds and cell complexes Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Optimization Sciences and techniques of general use Statistics Studies Tensors Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme |
| URI | https://www.proquest.com/docview/879722827 https://www.proquest.com/docview/1671311535 |
| Volume | 32 |
| WOSCitedRecordID | wos000292816300006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: 7WY dateStart: 19800301 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M0C dateStart: 19800301 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Agriculture Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M0K dateStart: 19800301 isFulltext: true titleUrlDefault: https://search.proquest.com/agriculturejournals providerName: ProQuest – providerCode: PRVPQU databaseName: Biological Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M7P dateStart: 19800301 isFulltext: true titleUrlDefault: http://search.proquest.com/biologicalscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: K7- dateStart: 19800301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M7S dateStart: 19800301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: Environmental Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: PATMY dateStart: 19800301 isFulltext: true titleUrlDefault: http://search.proquest.com/environmentalscience providerName: ProQuest – providerCode: PRVPQU databaseName: Materials Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: KB. dateStart: 19800301 isFulltext: true titleUrlDefault: http://search.proquest.com/materialsscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Military Database (ProQuest) customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M1Q dateStart: 19800301 isFulltext: true titleUrlDefault: https://search.proquest.com/military providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest - Research Library customDbUrl: eissn: 1095-7162 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M2O dateStart: 19880101 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest advanced technologies & aerospace journals customDbUrl: eissn: 1095-7162 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: P5Z dateStart: 19880101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1095-7162 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: BENPR dateStart: 19880101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1095-7162 dateEnd: 20140731 omitProxy: false ssIdentifier: ssj0016491 issn: 0895-4798 databaseCode: M2P dateStart: 19800301 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bj5QwFG7cXR80xrtxXJ1U44MPokALbZ8Ms3Z2yAwMAuOOvhAoJTHZzIzLrL_ftjAkG40vJuQLDQdCeno5l-Y7ALzFtYMrgbGF3cpTDkrpWhUtG8tjVJayrnxpQhdfFySO6XrNkv5sTtsfqzysiWahrrdCx8g_UsKIq_wD8mn309JFo3Ryta-gcQROlJ3MNHV-5HwZkgg-7grmUebpABLtiYUcTemjfEJfM2De2I7u7cpW9UzTlbT4Y3U2W870wX_-7ENwv7c1YdANjkfgltw8Bnejgai1fQIuJzzL4WJ5AaPVIg8XYcyDFKZBPIdBkqTLdRiZIBZcTuEsPJ_x1FJeI09hzuNsmWbv4STI-GeoJPIZh2nIoyCOw0A101WWWyk_129nmnmBPwWrKc_PZlZfgMESiHp7C7HGkQSJsmG4UnYWEr6ktU1qhKXrll5VEk8yp6EUswrZosFSVrVUZoWoqLAb9Awcb7Yb-RxARHBZE0dKjBkWrur_EkmslIYEllj4I_DuoIdC9OzkukjGZWG8FESKQWUj8GYQ3XWUHH8TGt9Q5iCpLBamzEp7BE4Pqiv6adsWg95G4PXwVM03nUQpN3J73RaOTwxDEfJe_PMLp-BOF37W10twvL-6lq_AbfFr_6O9GoMjcvFtDE4mPE5S1ZoTS-Pkg8LIPjM4H5vhrNFdGkwM5hqJuSeZwsT7_hvSvvOa |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bi9QwFA7rKqiId3FcXaMo-GBw2qRN-iDSdTPbMp3O0HZ03mqapiAsM-N2VvFH-R9NeoNF8W0fhL6Ungba8-Vc2-8A8IqUFikkIYjYhaMTFGGjgokKOR5TQpWFq5rSxaeIxjFbrbzFHvjV_wtjPqvsbWJjqMuNNDXyd4x61Nb5Af2w_YbM0CjTXO0naLSomKqfP3TGVr8Pj7V6X9v2hGcfA9QNFUASM2eHsFdZimIpKo8UOnbA0lWsHNMSE2XbwikEdZRnVYwRr8BjWRGlilJpVykLJscV1uteAVcJZtRsqylFQ9PCJe2APuY5pmDFOiIjy1AI6RzUNYybF9zfra2otSaqdoTGH96gcXGTO__Zy7kLbnexNPRb8N8De2p9H9ycDUS09QNwesTTDEbzz3C2jLIwCmPuJzDx4yn0F4tkvgpnTZEOzicwCE8CniCdFfMEZjxO50n6Fh75KT-GWiILOExCPvPjOPT1abJMM5TwE3N3apgl-EOwvJTHfQT215u1egwgpkSU1FKKEI9IW-tbYEUsHQ1Kooh0R-BNr_dcduzrZgjIad5kYZjmA0RG4OUgum0pR_4mdHgBPIOkjsg8HTaPR-Cgh0remaU6H3AyAi-Gq9qemCaRWKvNeZ1bLm0YmLDz5J8rPAfXg2wW5Vpx0wNwoy21m-Mp2N-dnatn4Jr8vvtanx02mwSCL5cNvN-_qkZ7 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=BEST+LOW+MULTILINEAR+RANK+APPROXIMATION+OF+HIGHER-ORDER+TENSORS%2C+BASED+ON+THE+RIEMANNIAN+TRUST-REGION+SCHEME&rft.jtitle=SIAM+journal+on+matrix+analysis+and+applications&rft.au=ISHTEVA%2C+Mariya&rft.au=ABSIL%2C+P.-A&rft.au=VAN+HUFFEL%2C+Sabine&rft.au=DE+LATHAUWER%2C+Lieven&rft.date=2011&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.issn=0895-4798&rft.volume=32&rft.issue=1&rft.spage=115&rft.epage=135&rft_id=info:doi/10.1137%2F090764827&rft.externalDBID=n%2Fa&rft.externalDocID=24190950 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0895-4798&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0895-4798&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0895-4798&client=summon |