Randomized algorithms for the computation of multilinear rank-(μ1,μ2,μ3) approximations
We present some randomized algorithms for computing multilinear rank- ( μ 1 , μ 2 , μ 3 ) approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse su...
Uloženo v:
| Vydáno v: | Journal of global optimization Ročník 87; číslo 2-4; s. 373 - 403 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.11.2023
Springer |
| Témata: | |
| ISSN: | 0925-5001, 1573-2916 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We present some randomized algorithms for computing multilinear rank-
(
μ
1
,
μ
2
,
μ
3
)
approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples. |
|---|---|
| AbstractList | We present some randomized algorithms for computing multilinear rank-
(
μ
1
,
μ
2
,
μ
3
)
approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples. We present some randomized algorithms for computing multilinear rank- [Formula omitted] approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples. |
| Audience | Academic |
| Author | Xu, Yanwei Che, Maolin Wei, Yimin |
| Author_xml | – sequence: 1 givenname: Maolin surname: Che fullname: Che, Maolin organization: School of Mathematics, Southwestern University of Finance and Economics – sequence: 2 givenname: Yimin surname: Wei fullname: Wei, Yimin email: ymwei@fudan.edu.cn organization: School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University – sequence: 3 givenname: Yanwei surname: Xu fullname: Xu, Yanwei organization: Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co., Ltd |
| BookMark | eNp9kM1KAzEURoNUsK2-gKtZKpiam3QmmWUp_kFBEN24CZlppk2dSYZkCuqz9Rn6TMaOKxflEi585OQLZ4QG1lmN0CWQCRDCbwMQkQtMKMUEQFAsTtAQUs4wzSEboCHJaYpTQuAMjULYEEJykdIhen9Rduka862XiapXzptu3YSkcj7p1jopXdNuO9UZZxNXJc227kxtrFY-8cp-4Kv9Dm72OxoPu05U23r3aZrD_XCOTitVB33xt8fo7f7udf6IF88PT_PZApeMkQ5rAQqgEKnIGYilqIArBXleTgVk0wKmZcXSqWZMcCpirgtFC55S4FBkeczHaNK_u1K1lsZWrvOqjLPUjSmjp8rEfMY5EA4ZSyNAe6D0LgSvK9n6-Gn_JYHIX52y1ymjTnnQKUWExD-oNL2Y2Gbq4yjr0RB77Ep7uXFbb6OTY9QPKKaNbg |
| CitedBy_id | crossref_primary_10_1109_TIP_2024_3385284 crossref_primary_10_1016_j_neucom_2025_130330 crossref_primary_10_1007_s10915_022_01956_y |
| Cites_doi | 10.1002/gamm.201310004 10.1137/S0895479898346995 10.1007/BF02289464 10.1137/090771806 10.1109/TSMC.2015.2482458 10.1109/ACCESS.2021.3058103 10.1016/j.ast.2009.12.003 10.1002/rsa.20218 10.1137/19M1261043 10.1137/S0895479896305696 10.1137/19M1237016 10.1137/17M1141977 10.1137/090764827 10.1137/110836067 10.1137/17M1111590 10.1561/0400000060 10.1137/19M1257718 10.1145/1186785.1186794 10.1016/S0304-3975(03)00400-6 10.1109/34.927464 10.1137/060673096 10.1016/j.jsc.2005.05.007 10.1007/978-981-15-2059-4 10.1145/2842602 10.1137/090763172 10.1007/s10444-018-9622-8 10.2514/1.35258 10.1137/07070111X 10.1145/1015706.1015725 10.1016/j.laa.2011.12.007 10.1137/070688316 10.1016/j.patcog.2006.08.004 10.1137/16M1093896 10.1016/j.camwa.2016.09.014 10.1137/15M1048628 10.1016/j.laa.2006.08.023 10.1016/j.acha.2007.12.002 10.1109/ICPR.2002.1048350 10.1137/1.9781611975482.172 10.1109/CVPR.2003.1211457 10.1007/s10444-020-09816-9 10.1137/100792056 10.1016/j.cam.2020.113380 10.1145/2488608.2488620 10.1002/9780470747278 10.1007/s10915-021-01545-5 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 COPYRIGHT 2023 Springer |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 – notice: COPYRIGHT 2023 Springer |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s10898-022-01182-8 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics Sciences (General) Computer Science |
| EISSN | 1573-2916 |
| EndPage | 403 |
| ExternalDocumentID | A771071635 10_1007_s10898_022_01182_8 |
| GrantInformation_xml | – fundername: national natural science foundation of china grantid: 11771099; 11901471 funderid: http://dx.doi.org/10.13039/501100001809 |
| GroupedDBID | -52 -57 -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29K 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYOK AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYQZM AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M0N M2O M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9M PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SBE SCLPG SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8T Z8U Z8W Z92 ZMTXR ZWQNP ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB |
| ID | FETCH-LOGICAL-c330t-e81a11b8589318d8f17aa199c48164b14cf354e338728199eba2b752171b69e33 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000801977100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0925-5001 |
| IngestDate | Sat Nov 29 10:30:57 EST 2025 Tue Nov 18 22:40:11 EST 2025 Sat Nov 29 01:59:36 EST 2025 Fri Feb 21 02:44:09 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2-4 |
| Keywords | approximation Multilinear rank 65F10 Singular values Randomized algorithms Sparse subspace embedding 65F15 Random projection The power scheme Singular value decomposition 15A18 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c330t-e81a11b8589318d8f17aa199c48164b14cf354e338728199eba2b752171b69e33 |
| PageCount | 31 |
| ParticipantIDs | gale_infotracacademiconefile_A771071635 crossref_primary_10_1007_s10898_022_01182_8 crossref_citationtrail_10_1007_s10898_022_01182_8 springer_journals_10_1007_s10898_022_01182_8 |
| PublicationCentury | 2000 |
| PublicationDate | 20231100 2023-11-00 20231101 |
| PublicationDateYYYYMMDD | 2023-11-01 |
| PublicationDate_xml | – month: 11 year: 2023 text: 20231100 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSubtitle | An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering |
| PublicationTitle | Journal of global optimization |
| PublicationTitleAbbrev | J Glob Optim |
| PublicationYear | 2023 |
| Publisher | Springer US Springer |
| Publisher_xml | – name: Springer US – name: Springer |
| References | Minster, Saibaba, Kilmer (CR32) 2020; 2 De Lathauwer, De Moor, Vandewalle (CR15) 2000; 21 Halko, Martinsson, Tropp (CR23) 2011; 53 CR39 CR33 Tucker (CR43) 1966; 31 Che, Wei (CR7) 2019; 45 CR30 Saibaba (CR35) 2016; 37 Ishteva, Absil, Van Huffel, De Lathauwer (CR24) 2011; 32 De Lathauwer, De Moor, Vandewalle (CR16) 2000; 21 Vasilescu, Terzopoulos (CR47) 2004; 23 CR5 Kolda, Bader (CR25) 2009; 51 Sun, Guo, Luo, Tropp, Udell (CR40) 2019; 2 Eldén, Savas (CR19) 2009; 31 CR48 CR46 Ailon, Chazelle (CR2) 2009; 39 Georghiades, Belhumeur, Kriegman (CR20) 2001; 23 CR45 Qi (CR34) 2005; 40 Drineas, Mahoney (CR17) 2007; 420 Vannieuwenhoven, Vandebril, Meerbergen (CR44) 2012; 34 Che, Wei, Yan (CR9) 2020; 41 Kressner, Perisa (CR26) 2017; 39 Yu, Gu, Li (CR51) 2018; 39 Ahmadiasl, Cichocki, Phan, Oseledets, Abukhovich, Tanaka (CR1) 2021; 9 Aizenbud, Shabat, Averbuch (CR3) 2016; 72 CR14 CR13 Savas, Eldén (CR36) 2007; 40 CR12 CR11 Mahoney (CR29) 2011; 3 CR10 Bader, Kolda (CR4) 2006; 32 CR52 Savas, Lim (CR38) 2010; 32 Che, Wei (CR8) 2020 Tropp, Yurtsever, Udell, Cevher (CR42) 2017; 38 Charikar, Chen, Farach-Colton (CR6) 2004; 312 Lorente, Vega, Velazquez (CR27) 2010; 14 Woolfe, Liberty, Rokhlin, Tygert (CR50) 2008; 25 Drineas, Mahoney (CR18) 2016; 59 Symeonidis (CR41) 2016; 46 CR21 Woodruff (CR49) 2014; 10 Matousek (CR31) 2008; 33 Lorente, Vega, Velazquez (CR28) 2010; 45 Savas, Eldén (CR37) 2013; 438 Grasedyck, Kressner, Tobler (CR22) 2013; 36 N Vannieuwenhoven (1182_CR44) 2012; 34 MW Mahoney (1182_CR29) 2011; 3 1182_CR48 AS Georghiades (1182_CR20) 2001; 23 1182_CR45 1182_CR46 M Vasilescu (1182_CR47) 2004; 23 M Ishteva (1182_CR24) 2011; 32 L De Lathauwer (1182_CR16) 2000; 21 M Che (1182_CR7) 2019; 45 B Savas (1182_CR36) 2007; 40 JA Tropp (1182_CR42) 2017; 38 M Charikar (1182_CR6) 2004; 312 1182_CR5 1182_CR39 1182_CR33 B Savas (1182_CR38) 2010; 32 L Grasedyck (1182_CR22) 2013; 36 L Eldén (1182_CR19) 2009; 31 1182_CR30 P Symeonidis (1182_CR41) 2016; 46 DP Woodruff (1182_CR49) 2014; 10 AK Saibaba (1182_CR35) 2016; 37 N Ailon (1182_CR2) 2009; 39 L Qi (1182_CR34) 2005; 40 P Drineas (1182_CR18) 2016; 59 1182_CR21 LR Tucker (1182_CR43) 1966; 31 BW Bader (1182_CR4) 2006; 32 Y Sun (1182_CR40) 2019; 2 B Savas (1182_CR37) 2013; 438 F Woolfe (1182_CR50) 2008; 25 M Che (1182_CR8) 2020 TG Kolda (1182_CR25) 2009; 51 LS Lorente (1182_CR28) 2010; 45 1182_CR11 LS Lorente (1182_CR27) 2010; 14 1182_CR12 N Halko (1182_CR23) 2011; 53 1182_CR13 1182_CR14 J Matousek (1182_CR31) 2008; 33 S Ahmadiasl (1182_CR1) 2021; 9 M Che (1182_CR9) 2020; 41 1182_CR52 1182_CR10 D Kressner (1182_CR26) 2017; 39 R Minster (1182_CR32) 2020; 2 W Yu (1182_CR51) 2018; 39 L De Lathauwer (1182_CR15) 2000; 21 Y Aizenbud (1182_CR3) 2016; 72 P Drineas (1182_CR17) 2007; 420 |
| References_xml | – ident: CR45 – volume: 36 start-page: 53 year: 2013 end-page: 78 ident: CR22 article-title: A literature survey of low-rank tensor approximation techniques publication-title: GAMM-Mitteilungen doi: 10.1002/gamm.201310004 – volume: 21 start-page: 1324 year: 2000 end-page: 1342 ident: CR16 article-title: On the best rank-1 and rank- approximation of higher-order tensors publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/S0895479898346995 – ident: CR39 – volume: 31 start-page: 279 year: 1966 end-page: 311 ident: CR43 article-title: Some mathematical notes on three-mode factor analysis publication-title: Psychometrika doi: 10.1007/BF02289464 – volume: 53 start-page: 217 year: 2011 end-page: 288 ident: CR23 article-title: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions publication-title: SIAM Review doi: 10.1137/090771806 – ident: CR12 – volume: 46 start-page: 1240 year: 2016 end-page: 1251 ident: CR41 article-title: ClustHOSVD: Item recommendation by combining semantically enhanced tag clustering with tensor HOSVD publication-title: IEEE Transactions on Systems, Man, and Cybernetics: Systems doi: 10.1109/TSMC.2015.2482458 – volume: 9 start-page: 28684 year: 2021 end-page: 28706 ident: CR1 article-title: Randomized algorithms for computation of Tucker decomposition and higher order SVD (HOSVD) publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3058103 – volume: 14 start-page: 168 year: 2010 end-page: 177 ident: CR27 article-title: Compression of aerodynamic databases using high-order singular value decomposition publication-title: Aerospace Science and Technology doi: 10.1016/j.ast.2009.12.003 – volume: 33 start-page: 142 year: 2008 end-page: 156 ident: CR31 article-title: On variants of the Johnson-Lindenstrauss lemma publication-title: Random Structures and Algorithms doi: 10.1002/rsa.20218 – ident: CR21 – ident: CR46 – volume: 2 start-page: 189 year: 2020 end-page: 215 ident: CR32 article-title: Randomized algorithms for low-rank tensor decompositions in the Tucker format publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/19M1261043 – volume: 21 start-page: 1253 year: 2000 end-page: 1278 ident: CR15 article-title: A multilinear singular value decomposition publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/S0895479896305696 – volume: 41 start-page: 605 year: 2020 end-page: 636 ident: CR9 article-title: The computation for low multilinear rank approximations of tensors via power scheme and random projection publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/19M1237016 – ident: CR11 – volume: 39 start-page: 1339 year: 2018 end-page: 1359 ident: CR51 article-title: Efficient randomized algorithms for the fixed-precision low-rank matrix approximation publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/17M1141977 – volume: 32 start-page: 115 year: 2011 end-page: 135 ident: CR24 article-title: Best low multilinear rank approximation of higher-order tensors, based on the Riemannian trust-region scheme publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/090764827 – ident: CR5 – volume: 34 start-page: A1027 year: 2012 end-page: A1052 ident: CR44 article-title: A new truncation strategy for the higher-order singular value decomposition publication-title: SIAM Journal on Scientific Computing doi: 10.1137/110836067 – volume: 38 start-page: 1454 year: 2017 end-page: 1485 ident: CR42 article-title: Practical sketching algorithms for low-rank matrix approximation publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/17M1111590 – volume: 10 start-page: 1 year: 2014 end-page: 157 ident: CR49 article-title: Sketching as a tool for numerical linear algebra publication-title: Foundations and Trends in Theoretical Computer Science doi: 10.1561/0400000060 – volume: 2 start-page: 1123 year: 2019 end-page: 1150 ident: CR40 article-title: Low-rank Tucker approximation of a tensor from streaming data publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/19M1257718 – volume: 32 start-page: 635 year: 2006 end-page: 653 ident: CR4 article-title: Algorithm 862: Matlab tensor classes for fast algorithm prototyping publication-title: ACM Transactions on Mathematical Software doi: 10.1145/1186785.1186794 – volume: 312 start-page: 3 year: 2004 end-page: 15 ident: CR6 article-title: Finding frequent items in data streams publication-title: Theoretical Computer Science doi: 10.1016/S0304-3975(03)00400-6 – volume: 23 start-page: 643 year: 2001 end-page: 660 ident: CR20 article-title: From few to many: illumination cone models for face recognition under variable lighting and pose publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence doi: 10.1109/34.927464 – volume: 3 start-page: 123 year: 2011 end-page: 224 ident: CR29 article-title: Randomized algorithms for matrices and data, Foundations and Trends in Machine publication-title: Learning – ident: CR14 – volume: 39 start-page: 302 year: 2009 end-page: 322 ident: CR2 article-title: The fast Johnson-Lindenstrauss transform and approximate nearest neighbors publication-title: SIAM Journal on Computing doi: 10.1137/060673096 – ident: CR30 – ident: CR10 – ident: CR33 – volume: 40 start-page: 1302 year: 2005 end-page: 1324 ident: CR34 article-title: Eigenvalues of a real supersymmetric tensor publication-title: Journal of Symbolic Computation doi: 10.1016/j.jsc.2005.05.007 – year: 2020 ident: CR8 publication-title: Theory and Computation of Complex Tensors and its Applications doi: 10.1007/978-981-15-2059-4 – volume: 59 start-page: 80 year: 2016 end-page: 90 ident: CR18 article-title: RandNLA: randomized numerical linear algebra publication-title: Comm. ACM doi: 10.1145/2842602 – volume: 32 start-page: 3352 year: 2010 end-page: 3393 ident: CR38 article-title: Quasi-Newton methods on Grassmannians and multilinear approximations of tensors publication-title: SIAM Journal on Scientific Computing doi: 10.1137/090763172 – volume: 45 start-page: 395 year: 2019 end-page: 428 ident: CR7 article-title: Randomized algorithms for the approximations of Tucker and the tensor train decompositions publication-title: Advances in Computational Mathematics doi: 10.1007/s10444-018-9622-8 – volume: 45 start-page: 1779 year: 2010 end-page: 1788 ident: CR28 article-title: Generation of aerodynamic databases using high-order singular value decomposition publication-title: Journal of Aircraft doi: 10.2514/1.35258 – volume: 51 start-page: 455 year: 2009 end-page: 500 ident: CR25 article-title: Tensor decompositions and applications publication-title: SIAM Review doi: 10.1137/07070111X – volume: 23 start-page: 336 year: 2004 end-page: 342 ident: CR47 article-title: Tensor Textures: Multilinear image-based rendering publication-title: ACM Transactions on Graphics doi: 10.1145/1015706.1015725 – volume: 438 start-page: 891 year: 2013 end-page: 918 ident: CR37 article-title: Krylov-type methods for tensor computations I publication-title: Linear Algebra and its Applications doi: 10.1016/j.laa.2011.12.007 – volume: 31 start-page: 248 year: 2009 end-page: 271 ident: CR19 article-title: A Newton-Grassmann method for computing the best multilinear rank- approximation of a tensor publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/070688316 – ident: CR48 – ident: CR52 – volume: 40 start-page: 993 year: 2007 end-page: 1003 ident: CR36 article-title: Handwritten digit classification using higher order singular value decomposition publication-title: Pattern Recognition doi: 10.1016/j.patcog.2006.08.004 – ident: CR13 – volume: 39 start-page: A1879 year: 2017 end-page: A1902 ident: CR26 article-title: Recompression of Hadamard products of tensors in Tucker format publication-title: SIAM Journal on Scientific Computing doi: 10.1137/16M1093896 – volume: 72 start-page: 2525 year: 2016 end-page: 2534 ident: CR3 article-title: Randomized LU decomposition using sparse projections publication-title: Computers and Mathematics with Applications doi: 10.1016/j.camwa.2016.09.014 – volume: 37 start-page: 1223 year: 2016 end-page: 1249 ident: CR35 article-title: HOID: higher order interpolatory decomposition for tensors based on Tucker representation publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/15M1048628 – volume: 420 start-page: 553 year: 2007 end-page: 571 ident: CR17 article-title: A randomized algorithm for a tensor-based generalization of the singular value decomposition publication-title: Linear Algebra and its Applications doi: 10.1016/j.laa.2006.08.023 – volume: 25 start-page: 335 year: 2008 end-page: 366 ident: CR50 article-title: A fast randomized algorithm for the approximation of matrices publication-title: Applied and Computational Harmonic Analysis doi: 10.1016/j.acha.2007.12.002 – ident: 1182_CR45 doi: 10.1109/ICPR.2002.1048350 – volume: 72 start-page: 2525 year: 2016 ident: 1182_CR3 publication-title: Computers and Mathematics with Applications doi: 10.1016/j.camwa.2016.09.014 – volume: 420 start-page: 553 year: 2007 ident: 1182_CR17 publication-title: Linear Algebra and its Applications doi: 10.1016/j.laa.2006.08.023 – volume: 59 start-page: 80 year: 2016 ident: 1182_CR18 publication-title: Comm. ACM doi: 10.1145/2842602 – volume: 312 start-page: 3 year: 2004 ident: 1182_CR6 publication-title: Theoretical Computer Science doi: 10.1016/S0304-3975(03)00400-6 – ident: 1182_CR39 doi: 10.1137/1.9781611975482.172 – volume: 46 start-page: 1240 year: 2016 ident: 1182_CR41 publication-title: IEEE Transactions on Systems, Man, and Cybernetics: Systems doi: 10.1109/TSMC.2015.2482458 – ident: 1182_CR46 doi: 10.1109/CVPR.2003.1211457 – volume: 9 start-page: 28684 year: 2021 ident: 1182_CR1 publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3058103 – volume: 45 start-page: 395 year: 2019 ident: 1182_CR7 publication-title: Advances in Computational Mathematics doi: 10.1007/s10444-018-9622-8 – volume: 25 start-page: 335 year: 2008 ident: 1182_CR50 publication-title: Applied and Computational Harmonic Analysis doi: 10.1016/j.acha.2007.12.002 – volume: 21 start-page: 1253 year: 2000 ident: 1182_CR15 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/S0895479896305696 – volume: 10 start-page: 1 year: 2014 ident: 1182_CR49 publication-title: Foundations and Trends in Theoretical Computer Science doi: 10.1561/0400000060 – ident: 1182_CR30 doi: 10.1007/s10444-020-09816-9 – ident: 1182_CR21 doi: 10.1137/100792056 – volume-title: Theory and Computation of Complex Tensors and its Applications year: 2020 ident: 1182_CR8 doi: 10.1007/978-981-15-2059-4 – volume: 2 start-page: 1123 year: 2019 ident: 1182_CR40 publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/19M1257718 – volume: 41 start-page: 605 year: 2020 ident: 1182_CR9 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/19M1237016 – volume: 2 start-page: 189 year: 2020 ident: 1182_CR32 publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/19M1261043 – ident: 1182_CR11 doi: 10.1016/j.cam.2020.113380 – volume: 31 start-page: 279 year: 1966 ident: 1182_CR43 publication-title: Psychometrika doi: 10.1007/BF02289464 – volume: 438 start-page: 891 year: 2013 ident: 1182_CR37 publication-title: Linear Algebra and its Applications doi: 10.1016/j.laa.2011.12.007 – volume: 3 start-page: 123 year: 2011 ident: 1182_CR29 publication-title: Learning – ident: 1182_CR14 doi: 10.1145/2488608.2488620 – ident: 1182_CR13 doi: 10.1002/9780470747278 – ident: 1182_CR33 – ident: 1182_CR12 – volume: 51 start-page: 455 year: 2009 ident: 1182_CR25 publication-title: SIAM Review doi: 10.1137/07070111X – volume: 33 start-page: 142 year: 2008 ident: 1182_CR31 publication-title: Random Structures and Algorithms doi: 10.1002/rsa.20218 – volume: 40 start-page: 993 year: 2007 ident: 1182_CR36 publication-title: Pattern Recognition doi: 10.1016/j.patcog.2006.08.004 – ident: 1182_CR48 – volume: 40 start-page: 1302 year: 2005 ident: 1182_CR34 publication-title: Journal of Symbolic Computation doi: 10.1016/j.jsc.2005.05.007 – volume: 31 start-page: 248 year: 2009 ident: 1182_CR19 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/070688316 – volume: 36 start-page: 53 year: 2013 ident: 1182_CR22 publication-title: GAMM-Mitteilungen doi: 10.1002/gamm.201310004 – volume: 39 start-page: 302 year: 2009 ident: 1182_CR2 publication-title: SIAM Journal on Computing doi: 10.1137/060673096 – volume: 53 start-page: 217 year: 2011 ident: 1182_CR23 publication-title: SIAM Review doi: 10.1137/090771806 – volume: 23 start-page: 336 year: 2004 ident: 1182_CR47 publication-title: ACM Transactions on Graphics doi: 10.1145/1015706.1015725 – volume: 34 start-page: A1027 year: 2012 ident: 1182_CR44 publication-title: SIAM Journal on Scientific Computing doi: 10.1137/110836067 – volume: 37 start-page: 1223 year: 2016 ident: 1182_CR35 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/15M1048628 – volume: 21 start-page: 1324 year: 2000 ident: 1182_CR16 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/S0895479898346995 – volume: 39 start-page: 1339 year: 2018 ident: 1182_CR51 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/17M1141977 – volume: 39 start-page: A1879 year: 2017 ident: 1182_CR26 publication-title: SIAM Journal on Scientific Computing doi: 10.1137/16M1093896 – volume: 23 start-page: 643 year: 2001 ident: 1182_CR20 publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence doi: 10.1109/34.927464 – volume: 32 start-page: 635 year: 2006 ident: 1182_CR4 publication-title: ACM Transactions on Mathematical Software doi: 10.1145/1186785.1186794 – volume: 32 start-page: 3352 year: 2010 ident: 1182_CR38 publication-title: SIAM Journal on Scientific Computing doi: 10.1137/090763172 – volume: 32 start-page: 115 year: 2011 ident: 1182_CR24 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/090764827 – volume: 45 start-page: 1779 year: 2010 ident: 1182_CR28 publication-title: Journal of Aircraft doi: 10.2514/1.35258 – ident: 1182_CR10 doi: 10.1007/s10915-021-01545-5 – volume: 38 start-page: 1454 year: 2017 ident: 1182_CR42 publication-title: SIAM Journal on Matrix Analysis and Applications doi: 10.1137/17M1111590 – volume: 14 start-page: 168 year: 2010 ident: 1182_CR27 publication-title: Aerospace Science and Technology doi: 10.1016/j.ast.2009.12.003 – ident: 1182_CR5 – ident: 1182_CR52 |
| SSID | ssj0009852 |
| Score | 2.3974557 |
| Snippet | We present some randomized algorithms for computing multilinear rank-
(
μ
1
,
μ
2
,
μ
3
)
approximations of tensors by combining the sparse subspace embedding... We present some randomized algorithms for computing multilinear rank- [Formula omitted] approximations of tensors by combining the sparse subspace embedding... |
| SourceID | gale crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 373 |
| SubjectTerms | Algorithms Analysis Computer Science Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Real Functions |
| Title | Randomized algorithms for the computation of multilinear rank-(μ1,μ2,μ3) approximations |
| URI | https://link.springer.com/article/10.1007/s10898-022-01182-8 |
| Volume | 87 |
| WOSCitedRecordID | wos000801977100001&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-2916 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1dSxwxFL1U64N9qHW1dGtb8iBU0cBmkpjkUUqlL5VS2yK-DPkaXdDdsrNK6W_zN_ibvMlm_AAR9GEeZkgyITe5OZfkngOw7mQcuKpiNAhVUYEejxqrOOVSMOa8CFq5LDah9vf14aH5UZLC2u62e3ckmT31nWQ3ndLBqnSVAFEx1XPwUia2mRSjH_y5pdrVWWdnYCpJJXrhkirzcBv3tqPOKd8_Es07zd7S8_r4Bl4XZEl2Z1NhGV7EUQ-WOtUGUhZxD17doSDEt-83vK1tD5ZLqZZsFD7qzRU4-mlHYXw2_B8DsafH48lwenLWEkS7BKsSn_-QDUzGDck3FBN2tROSBOHpxtUl2766rPDhmyRzmP8bzhIm21X4vff115dvtEgyUM_5YEqjZhZtqCXCHKaDbpiylhnjhca4yzHhG7RyxLhXpRM6E52tnEKIoJjbMfj9LcyPxqP4DkhjJRdRem9CEL4KdqdpuNBm4I3jPjR9YJ1lal_4ypNsxml9y7ScRrvG0a7zaNe6D1s3df7O2DoeLf05GbxOSxlb9rZkJGD_EilWvasQfmE8yWUftjt712WNt480_P5pxddgMYnYzzIcP8D8dHIeP8KCv5gO28mnPLmvAdyg8uc |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1baxQxFD5oFawPrV1b3HrLg2CLDWwmmSZ5LMVSsV1EqxRfQm6jC-2u7Kwi_W39Df1NnmQzvYAU9GEeZkgyISc5-Q7J-T6AV66OA1dVjAYhKyrQ41FtJae8Fow5L4KSLotNyOFQHR_rDyUprO1uu3dHktlTX0t2UykdrEpXCRAVU3UX7okks5Ni9E9frqh2VdbZGeiqpjV64ZIq8_c2bmxHnVO-eSSad5q95f_r4yNYKsiS7MynwgrcieMeLHeqDaQs4h48vEZBiG-Hl7ytbQ9WSqmWbBQ-6s3H8PWjHYfJ6egsBmJPvk2mo9n305Yg2iVYlfj8h2xgMmlIvqGYsKudkiQITzcuztnWxXmFD98kmcP892ieMNmuwue9t0e7-7RIMlDP-WBGo2IWbahqhDlMBdUwaS3T2guFcZdjwjdo5Yhxr0wndDo6WzmJEEEyt63x-xosjCfj-ARIY2suYu29DkH4KtjtpuFC6YHXjvvQ9IF1ljG-8JUn2YwTc8W0nEbb4GibPNpG9eHNZZ0fc7aOW0u_TgY3aSljy96WjATsXyLFMjsS4RfGk7zuw1Znb1PWeHtLw-v_VvwlPNg_OjwwB--G75_CYhK0n2c7PoOF2fRnfA73_a_ZqJ2-yBP9D0b39cs |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1daxQxFL1oFdEHa9eKa6vmQbDFhm4mmSZ5LNVFUZdSPyi-DJkkowvtbNkZRfrb-hv6m7zJZNotSEF8mIcZkkzIzce55J5zAV6UuR-VWcaoEzKjAnc8qo3klOeCsdIKp2QZk03IyUQdHur9BRZ_jHbvryQ7TkNQaarb7RNXbS8Q31SghmUhrAARMlU34ZZATyYEdR18-nopu6tizp2RznKa446caDN_b-PK0dRv0FevR-OpM17-__4-gPsJcZLdboqswA1fD2C5z-ZA0uIewL0FaUJ8-3ih59oMYCWVashG0qnefAjfDkztZsfTU--IOfo-m0_bH8cNQRRMsCqx8Q_R8GRWkRi5GDCtmZOQKJ5unJ-xrfOzDB--SaK2-e9pR6RsVuHL-M3nvbc0pWqglvNRS71iBm2rcoQ_TDlVMWkM09oKhf5YyYSt0Poe_WEZbu60L01WSoQOkpU7Gr8_gqV6VvvHQCqTc-Fza7VzwmbO7FQVF0qPrC65ddUQWG-lwiYd85BO46i4VGAOo13gaBdxtAs1hFcXdU46FY9rS78Mxi_CEseWrUlMBexfEMsqdiXCMvQzeT6Erd72RVr7zTUNP_m34s_hzv7rcfHh3eT9GtwNee47EuQ6LLXzn_4p3La_2mkzfxbn_B_rQ_6v |
| 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=Randomized+algorithms+for+the+computation+of+multilinear+rank-%24%24%28%5Cmu+_1%2C%5Cmu+_2%2C%5Cmu+_3%29%24%24+approximations&rft.jtitle=Journal+of+global+optimization&rft.au=Che%2C+Maolin&rft.au=Wei%2C+Yimin&rft.au=Xu%2C+Yanwei&rft.date=2023-11-01&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=87&rft.issue=2-4&rft.spage=373&rft.epage=403&rft_id=info:doi/10.1007%2Fs10898-022-01182-8&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10898_022_01182_8 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon |