Paved with good intentions: Analysis of a randomized block Kaczmarz method
The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a block Kaczmarz algorithm that uses a randomized control scheme t...
Saved in:
| Published in | Linear algebra and its applications Vol. 441; pp. 199 - 221 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.01.2014
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a block Kaczmarz algorithm that uses a randomized control scheme to choose the subset at each step. This algorithm is the first block Kaczmarz method with an (expected) linear rate of convergence that can be expressed in terms of the geometric properties of the matrix and its submatrices. The analysis reveals that the algorithm is most effective when it is given a good row paving of the matrix, a partition of the rows into well-conditioned blocks. The operator theory literature provides detailed information about the existence and construction of good row pavings. Together, these results yield an efficient block Kaczmarz scheme that applies to many overdetermined least-squares problem. |
|---|---|
| AbstractList | The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a block Kaczmarz algorithm that uses a randomized control scheme to choose the subset at each step. This algorithm is the first block Kaczmarz method with an (expected) linear rate of convergence that can be expressed in terms of the geometric properties of the matrix and its submatrices. The analysis reveals that the algorithm is most effective when it is given a good row paving of the matrix, a partition of the rows into well-conditioned blocks. The operator theory literature provides detailed information about the existence and construction of good row pavings. Together, these results yield an efficient block Kaczmarz scheme that applies to many overdetermined least-squares problem. |
| Author | Tropp, Joel A. Needell, Deanna |
| Author_xml | – sequence: 1 givenname: Deanna surname: Needell fullname: Needell, Deanna email: dneedell@cmc.edu organization: Dept. of Mathematics and Computer Science, Claremont McKenna College, Claremont, CA 91711, USA – sequence: 2 givenname: Joel A. surname: Tropp fullname: Tropp, Joel A. email: jtropp@acm.caltech.edu organization: Applied and Computational Mathematics, MC 217-50, California Inst. Technology, Pasadena, CA 91125, USA |
| BookMark | eNp9kM1OAyEURonRxLb6AO54gakXmDKMrprG_ya60DWhwFjqFAyQmvbppakrF02-5G7uubnfGaJTH7xF6IrAmADh16txr9SYAqHjEqD0BA2IaFhFxISfogEArSvWtJNzNExpBQB1A3SAnt_Uxhr84_ISf4ZgsPPZ-uyCTzd46lW_TS7h0GGFo_ImrN2urC_6oL_wi9K7tYo7vLZ5GcwFOutUn-zl3xyhj_u799ljNX99eJpN55VmNeRqomvggplWKc2E5kJxajntaE0aWLQACkStF12nNDFGN6LRljLdcsoNZcKwESKHuzqGlKLt5Hd05Y-tJCD3MuRKFhlyL0OWFBmFaf4x2mW1r5mjcv1R8vZA2lJp42yUSTvrtTUuWp2lCe4I_QvlDnuy |
| CitedBy_id | crossref_primary_10_1137_18M1179249 crossref_primary_10_1016_j_amc_2023_127892 crossref_primary_10_3390_sym14010113 crossref_primary_10_1109_LSP_2013_2294376 crossref_primary_10_1137_21M1463306 crossref_primary_10_1016_j_amc_2023_128468 crossref_primary_10_3934_nhm_2024062 crossref_primary_10_1002_cpe_8274 crossref_primary_10_1109_LSP_2015_2412253 crossref_primary_10_1016_j_cam_2023_115333 crossref_primary_10_1016_j_laa_2015_03_028 crossref_primary_10_3934_math_2023941 crossref_primary_10_2298_FIL2314603Z crossref_primary_10_1016_j_cam_2021_113828 crossref_primary_10_1007_s11075_024_01872_2 crossref_primary_10_1002_nla_2470 crossref_primary_10_1002_nla_2591 crossref_primary_10_3934_math_2024122 crossref_primary_10_1007_s10107_021_01649_8 crossref_primary_10_1007_s40314_022_01978_0 crossref_primary_10_1093_imanum_drae033 crossref_primary_10_1007_s10107_019_01438_4 crossref_primary_10_1016_j_aml_2024_109027 crossref_primary_10_1016_j_laa_2024_06_010 crossref_primary_10_1137_16M1077891 crossref_primary_10_1016_j_cam_2018_02_025 crossref_primary_10_1137_23M1545537 crossref_primary_10_1007_s10543_024_01024_x crossref_primary_10_1007_s11075_024_01982_x crossref_primary_10_1016_j_cam_2023_115065 crossref_primary_10_1137_21M1429187 crossref_primary_10_1017_S0962492920000021 crossref_primary_10_1007_s42967_024_00447_1 crossref_primary_10_1364_AO_54_000C23 crossref_primary_10_1093_imaiai_iaab017 crossref_primary_10_1007_s00365_015_9303_5 crossref_primary_10_1088_1361_6420_aca78a crossref_primary_10_1007_s11075_017_0425_7 crossref_primary_10_1016_j_jfranklin_2022_09_028 crossref_primary_10_1016_j_laa_2024_10_009 crossref_primary_10_1016_j_amc_2019_124907 crossref_primary_10_1007_s12190_024_02060_0 crossref_primary_10_1016_j_cam_2024_116328 crossref_primary_10_1088_1361_6420_ac5f76 crossref_primary_10_1007_s40314_023_02232_x crossref_primary_10_1007_s11075_020_00895_9 crossref_primary_10_1016_j_jcp_2024_113351 crossref_primary_10_1016_j_cam_2023_115439 crossref_primary_10_1137_22M148803X crossref_primary_10_1137_20M1312629 crossref_primary_10_1016_j_sigpro_2024_109736 crossref_primary_10_1002_nla_2560 crossref_primary_10_1007_s40314_024_02819_y crossref_primary_10_1109_TIT_2024_3420222 crossref_primary_10_1016_j_cam_2021_113577 crossref_primary_10_1007_s11075_023_01661_3 crossref_primary_10_1007_s10092_021_00429_2 crossref_primary_10_1007_s11075_022_01473_x crossref_primary_10_1016_j_laa_2024_07_009 crossref_primary_10_1137_20M1350947 crossref_primary_10_1007_s40314_024_02967_1 crossref_primary_10_1016_j_laa_2014_11_035 crossref_primary_10_1137_19M1307044 crossref_primary_10_1137_19M1251643 crossref_primary_10_1137_24M1633820 crossref_primary_10_1007_s10107_015_0864_7 crossref_primary_10_1093_gji_ggv020 crossref_primary_10_1155_2014_908984 crossref_primary_10_1007_s10957_016_0867_4 crossref_primary_10_1016_j_apnum_2024_04_016 crossref_primary_10_1109_TCI_2020_3032101 crossref_primary_10_1137_18M1179213 crossref_primary_10_1088_1361_6420_ab2787 crossref_primary_10_1109_JSAIT_2024_3384395 crossref_primary_10_1109_LSP_2016_2590468 crossref_primary_10_1109_TIT_2024_3422918 crossref_primary_10_1007_s10543_023_01002_9 crossref_primary_10_1088_1361_6420_ac1778 crossref_primary_10_1007_s11075_021_01104_x crossref_primary_10_1137_23M155493X crossref_primary_10_1007_s42967_024_00427_5 crossref_primary_10_1007_s00521_018_3779_4 crossref_primary_10_1137_15M1025487 crossref_primary_10_12677_AAM_2024_131046 crossref_primary_10_1016_j_aml_2023_108704 crossref_primary_10_1137_23M155712X crossref_primary_10_1007_s10092_025_00639_y crossref_primary_10_3934_era_2022062 crossref_primary_10_3934_math_2025286 crossref_primary_10_1007_s13160_023_00620_8 crossref_primary_10_4236_jamp_2021_911189 crossref_primary_10_14498_vsgtu1548 crossref_primary_10_1007_s11075_024_01844_6 crossref_primary_10_1088_0266_5611_31_12_125008 crossref_primary_10_1007_s42967_023_00358_7 crossref_primary_10_1016_j_laa_2020_10_035 crossref_primary_10_1007_s43069_023_00269_6 crossref_primary_10_1137_22M1517196 crossref_primary_10_1002_nla_2429 crossref_primary_10_3934_math_20241614 crossref_primary_10_1137_21M1398562 crossref_primary_10_1016_j_laa_2023_03_003 crossref_primary_10_3934_math_2022378 crossref_primary_10_1137_16M1073807 crossref_primary_10_1007_s10092_021_00404_x crossref_primary_10_3390_math10142408 crossref_primary_10_1007_s11075_023_01684_w crossref_primary_10_1137_19M129111X crossref_primary_10_1007_s10543_021_00877_w crossref_primary_10_3934_nhm_2024014 crossref_primary_10_1088_1361_6420_ad5fb1 crossref_primary_10_1088_0266_5611_30_5_055007 crossref_primary_10_1088_1361_6420_ad5583 crossref_primary_10_1137_22M1488715 crossref_primary_10_1007_s10107_017_1229_1 crossref_primary_10_1007_s11075_016_0118_7 crossref_primary_10_1007_s11075_016_0176_x crossref_primary_10_1137_15M1014425 crossref_primary_10_1016_j_apnum_2023_06_008 crossref_primary_10_1007_s11075_023_01540_x crossref_primary_10_1109_TIT_2021_3113285 crossref_primary_10_1016_j_eswa_2021_116296 crossref_primary_10_1016_j_laa_2019_05_005 crossref_primary_10_1016_j_laa_2022_07_003 crossref_primary_10_1080_10556788_2021_1998492 crossref_primary_10_1002_nla_2377 crossref_primary_10_1137_130920642 crossref_primary_10_1007_s11075_024_01945_2 crossref_primary_10_1002_mma_9931 crossref_primary_10_1007_s40314_022_02044_5 crossref_primary_10_1016_j_amc_2022_127339 crossref_primary_10_1007_s10092_023_00549_x crossref_primary_10_1137_23M1575883 crossref_primary_10_1016_j_aml_2024_109053 crossref_primary_10_1016_j_cam_2020_113099 crossref_primary_10_1007_s10994_022_06140_9 crossref_primary_10_1007_s11075_024_01972_z crossref_primary_10_1090_qam_1587 crossref_primary_10_1002_mma_7990 crossref_primary_10_3934_era_2024178 crossref_primary_10_1007_s10092_024_00628_7 crossref_primary_10_1016_j_aml_2020_106294 crossref_primary_10_1093_imaiai_iaab029 crossref_primary_10_1088_1361_6420_ab77da crossref_primary_10_1007_s11075_024_01907_8 crossref_primary_10_1007_s40314_023_02453_0 crossref_primary_10_12677_aam_2025_142067 crossref_primary_10_1016_j_apnum_2023_01_013 crossref_primary_10_1137_18M1230323 crossref_primary_10_1137_19M125248X crossref_primary_10_1016_j_laa_2021_01_024 crossref_primary_10_1007_s11075_021_01143_4 crossref_primary_10_1007_s10589_020_00220_z crossref_primary_10_1080_01630563_2021_2001822 crossref_primary_10_1137_20M1352235 crossref_primary_10_1002_nla_2233 crossref_primary_10_1016_j_cam_2022_114372 crossref_primary_10_1137_19M1285846 crossref_primary_10_1007_s10851_014_0539_7 crossref_primary_10_1016_j_amc_2021_126373 crossref_primary_10_3390_math10234594 crossref_primary_10_1090_mcom_3818 crossref_primary_10_1088_1361_6560_ad56f1 crossref_primary_10_1007_s10444_023_10018_2 crossref_primary_10_4236_jamp_2021_912196 crossref_primary_10_1007_s10107_019_01404_0 crossref_primary_10_1109_TIT_2022_3202733 |
| Cites_doi | 10.1112/S0025579313000144 10.1007/s00041-009-9077-x 10.1109/18.959265 10.5642/tspmcos.2012.01 10.1007/BF02772174 10.1007/BF02809903 10.1090/S0894-0347-02-00398-3 10.1016/0022-247X(78)90214-7 10.1016/0022-5193(70)90109-8 10.1016/j.spl.2012.03.038 10.1007/BF03011619 10.1137/120874540 10.1007/BF01396365 10.1214/aoms/1177693335 10.1023/A:1022398014630 10.1007/s00041-008-9030-4 10.1142/S1793536911000787 10.1073/pnas.0507888103 10.1007/s11075-011-9451-z 10.1016/0024-3795(89)90375-3 10.1016/0024-3795(81)90139-7 10.2307/2372748 10.1007/BF02510922 10.1137/1.9781611973068.106 10.1287/moor.1100.0456 10.1007/s10208-011-9099-z 10.1007/s10107-012-0614-z 10.1137/090771806 10.1007/s00041-009-9082-0 10.1007/BF01236652 10.1007/s11856-011-0194-2 10.1007/s10543-010-0265-5 10.1137/060673096 10.1109/42.241889 10.1214/aop/1176989118 10.1016/0022-247X(87)90352-0 10.1137/090767911 10.1016/j.crma.2008.10.008 10.1137/120889897 10.1117/12.131447 10.1016/j.acha.2007.12.002 10.4064/sm185-1-4 10.1007/BF01581245 |
| ContentType | Journal Article |
| Copyright | 2013 Elsevier Inc. |
| Copyright_xml | – notice: 2013 Elsevier Inc. |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.laa.2012.12.022 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1873-1856 |
| EndPage | 221 |
| ExternalDocumentID | 10_1016_j_laa_2012_12_022 S0024379513000098 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 8P~ 9JN AACTN AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AASFE AAXUO ABAOU ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM M26 M41 MCRUF MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RIG RNS ROL RPZ SDF SDG SES SPC SPCBC SSW SSZ T5K TN5 TWZ WH7 XPP YQT ZMT ~G- 29L AAEDT AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ACRPL ACVFH ADCNI ADIYS ADMUD ADNMO ADVLN AEIPS AETEA AEUPX AFFNX AFJKZ AFPUW AFXIZ AGCQF AGHFR AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BNPGV CITATION EJD FA8 FGOYB G-2 HZ~ MVM OHT R2- SEW SSH T9H WUQ |
| ID | FETCH-LOGICAL-c340t-5c40683d9aac38c68a62e62f24170b900a084cbffac1ddc787ce23c9626d238d3 |
| IEDL.DBID | .~1 |
| ISSN | 0024-3795 |
| IngestDate | Tue Jul 01 03:17:57 EDT 2025 Thu Apr 24 23:02:26 EDT 2025 Fri Feb 23 02:35:54 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 68W20 65F10 65F20 41A65 Block Kaczmarz Projections onto convex sets Matrix paving Algebraic reconstruction technique |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c340t-5c40683d9aac38c68a62e62f24170b900a084cbffac1ddc787ce23c9626d238d3 |
| OpenAccessLink | https://www.sciencedirect.com/science/article/pii/S0024379513000098 |
| PageCount | 23 |
| ParticipantIDs | crossref_primary_10_1016_j_laa_2012_12_022 crossref_citationtrail_10_1016_j_laa_2012_12_022 elsevier_sciencedirect_doi_10_1016_j_laa_2012_12_022 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2014-01-15 |
| PublicationDateYYYYMMDD | 2014-01-15 |
| PublicationDate_xml | – month: 01 year: 2014 text: 2014-01-15 day: 15 |
| PublicationDecade | 2010 |
| PublicationTitle | Linear algebra and its applications |
| PublicationYear | 2014 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | E. Liberty, Accelerated dense random projections, Ph.D. dissertation, Yale University, New Haven, CT, 2009. Leventhal, Lewis (b0175) 2010; 35 Popa (b0215) 2004; 12 M. Benzi, Key moments in the history of numerical analysis, Presented at 2009 SIAM Applied Linear Algebra Conference, October 2009. B. Kashin, L. Tzafriri, Some remarks on coordinate restriction of operators to coordinate subspaces, Institute of Mathematics Preprint 12, Hebrew University, Jerusalem, 1993–1994. Tropp (b0275) 2012; 12 Bai, Yin (b0055) 1993; 21 R. Aharoni, Y. Censor, Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, in: Proceedings of the Fourth Haifa Matrix Theory Conference (Haifa, 1988), vol. 120, 1989, pp. 165–175. Tropp (b0255) 2008; 346 Bourgain, Tzafriri (b0045) 1987; 57 H.G. Feichtinger, T. Strohmer, A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices, in: SampTA ’95: 1995 Workshop on Sampling Theory and Applications, Jurmala, Latvia, September 1995, pp. 32–37. Hamaker, Solmon (b0145) 1978; 62 Hanson, Wright (b0150) 1971; 42 Vershynin (b0285) 2001; 122 Tropp (b0270) 2011; 3 S. Foucart, H. Rauhut, A Mathematical Introduction to Compressive Sensing, Birkha, Applied and Numerical Harmonic Analysis, in press. Popa (b0200) 1998; 38 C. Boutsidis, A. Gittens, Improved matrix algorithms via the Subsampled Randomized Hadamard Transform. A. Zouzias, N.M. Freris, Randomized extended Kaczmarz for solving least-squares. Ailon, Chazelle (b0010) 2009; 39 Berman, Halpern, Kaftal, Weiss (b0035) 1988; 11 Sezan, Stark (b0235) 1987; 122 Xu, Zikatanov (b0300) 2002; 15 Chen, Powell (b0080) 2012 Popa (b0210) 2001; 8 Gordon, Bender, Herman (b0125) 1970; 29 Avron, Maymounkov, Toledo (b0015) 2010; 32 P. Youssef, A note on column subset selection. Needell (b0190) 2010; 50 Björck (b0040) 1996 Anderson (b0020) 1979; 249 Byrne (b0060) 2008 May 2012. Herman, Meyer (b0135) 1993; 12 C.F. Gauss, Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Supplementum, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), 1995 (Transl. G.W. Stewart). J.A. Tropp, Column subset selection, matrix factorization, and eigenvalue optimization, in: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, 2009, pp. 978–986. Casazza, Tremain (b0085) 2006; 103 April 2011. G.H. Golub, C.F. Van Loan, Matrix computations, Johns Hopkins Studies in the Mathematical Sciences, third ed., Johns Hopkins University Press, Baltimore, MD, 1996. Strohmer, Vershynin (b0250) 2009; 15 D. Needell, R. Ward, Two-subspace projection method for coherent overdetermined linear systems. Popa (b0205) 1999; 39 Strohmer, Vershynin (b0245) 2009; 15 Spielman, Srivastava (b0240) 2012; 190 Eldar, Needell (b0105) 2011; 58 Kadison, Singer (b0160) 1959; 81 Halko, Martinsson, Tropp (b0140) 2011; 53 December 2012. Censor, Herman, Jiang (b0075) 2009; 15 Kaczmarz (b0155) 1937; 29 Bourgain, Tzafriri (b0050) 1991; 420 Eggermont, Herman, Lent (b0095) 1981; 40 Elfving (b0100) 1980; 35 P. Youssef, Restricted invertibility and the Banach–Mazur distance to the cube. A. Naor, Sparse quadratic forms and their geometric applications, Technical Report No. 1033, Séminaire Bourbaki, January 2011. April 2012. Chrétien, Darses (b0065) 2012; 82 Woolfe, Liberty, Rokhlin, Tygert (b0295) 2008; 25 B. Recht, C. Ré, Beneath the valley of the noncommutative arithmetic–geometric mean inequality: conjectures, case studies, and consequences, in: Proceedings of the 25th Annual Conference on Learning Theory, Edinburgh, June 2012. C. Cenker, H.G. Feichtinger, M. Mayer, H. Steier, T. Strohmer, New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling, in: Proceedings of the SPIE: Visual Communications and Image Processing, 1992, pp. 299–310. Tseng (b0280) 1993; 59 P. Richtárik, M. Takáč, Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Tropp (b0260) 2008; 185 Vershynin (b0290) 2006; vol. 51 June 2012. Natterer (b0185) 2001; vol. 32 Donoho, Huo (b0090) 2001; 47 N. Srivastava, Spectral sparsification and restricted invertibility, Ph.D. dissertation, Yale University, New Haven, CT, 2010. Chrétien (10.1016/j.laa.2012.12.022_b0065) 2012; 82 Tropp (10.1016/j.laa.2012.12.022_b0255) 2008; 346 Björck (10.1016/j.laa.2012.12.022_b0040) 1996 Vershynin (10.1016/j.laa.2012.12.022_b0290) 2006; vol. 51 Eldar (10.1016/j.laa.2012.12.022_b0105) 2011; 58 Avron (10.1016/j.laa.2012.12.022_b0015) 2010; 32 Natterer (10.1016/j.laa.2012.12.022_b0185) 2001; vol. 32 Kadison (10.1016/j.laa.2012.12.022_b0160) 1959; 81 10.1016/j.laa.2012.12.022_b0165 10.1016/j.laa.2012.12.022_b0120 10.1016/j.laa.2012.12.022_b0005 Sezan (10.1016/j.laa.2012.12.022_b0235) 1987; 122 10.1016/j.laa.2012.12.022_b0070 10.1016/j.laa.2012.12.022_b0030 Elfving (10.1016/j.laa.2012.12.022_b0100) 1980; 35 10.1016/j.laa.2012.12.022_b0195 10.1016/j.laa.2012.12.022_b0110 Hamaker (10.1016/j.laa.2012.12.022_b0145) 1978; 62 Popa (10.1016/j.laa.2012.12.022_b0200) 1998; 38 10.1016/j.laa.2012.12.022_b0230 10.1016/j.laa.2012.12.022_b0310 Berman (10.1016/j.laa.2012.12.022_b0035) 1988; 11 Vershynin (10.1016/j.laa.2012.12.022_b0285) 2001; 122 Donoho (10.1016/j.laa.2012.12.022_b0090) 2001; 47 10.1016/j.laa.2012.12.022_b0115 Casazza (10.1016/j.laa.2012.12.022_b0085) 2006; 103 Leventhal (10.1016/j.laa.2012.12.022_b0175) 2010; 35 10.1016/j.laa.2012.12.022_b0315 Byrne (10.1016/j.laa.2012.12.022_b0060) 2008 Woolfe (10.1016/j.laa.2012.12.022_b0295) 2008; 25 Strohmer (10.1016/j.laa.2012.12.022_b0245) 2009; 15 Bai (10.1016/j.laa.2012.12.022_b0055) 1993; 21 Tseng (10.1016/j.laa.2012.12.022_b0280) 1993; 59 Bourgain (10.1016/j.laa.2012.12.022_b0045) 1987; 57 Tropp (10.1016/j.laa.2012.12.022_b0270) 2011; 3 10.1016/j.laa.2012.12.022_b0180 Hanson (10.1016/j.laa.2012.12.022_b0150) 1971; 42 Anderson (10.1016/j.laa.2012.12.022_b0020) 1979; 249 Popa (10.1016/j.laa.2012.12.022_b0210) 2001; 8 10.1016/j.laa.2012.12.022_b0220 Spielman (10.1016/j.laa.2012.12.022_b0240) 2012; 190 Gordon (10.1016/j.laa.2012.12.022_b0125) 1970; 29 10.1016/j.laa.2012.12.022_b0265 10.1016/j.laa.2012.12.022_b0025 10.1016/j.laa.2012.12.022_b0225 10.1016/j.laa.2012.12.022_b0305 Halko (10.1016/j.laa.2012.12.022_b0140) 2011; 53 Xu (10.1016/j.laa.2012.12.022_b0300) 2002; 15 Ailon (10.1016/j.laa.2012.12.022_b0010) 2009; 39 Strohmer (10.1016/j.laa.2012.12.022_b0250) 2009; 15 Tropp (10.1016/j.laa.2012.12.022_b0260) 2008; 185 10.1016/j.laa.2012.12.022_b0170 Bourgain (10.1016/j.laa.2012.12.022_b0050) 1991; 420 Chen (10.1016/j.laa.2012.12.022_b0080) 2012 10.1016/j.laa.2012.12.022_b0130 Tropp (10.1016/j.laa.2012.12.022_b0275) 2012; 12 Censor (10.1016/j.laa.2012.12.022_b0075) 2009; 15 Popa (10.1016/j.laa.2012.12.022_b0215) 2004; 12 Herman (10.1016/j.laa.2012.12.022_b0135) 1993; 12 Eggermont (10.1016/j.laa.2012.12.022_b0095) 1981; 40 Popa (10.1016/j.laa.2012.12.022_b0205) 1999; 39 Needell (10.1016/j.laa.2012.12.022_b0190) 2010; 50 Kaczmarz (10.1016/j.laa.2012.12.022_b0155) 1937; 29 |
| References_xml | – reference: B. Recht, C. Ré, Beneath the valley of the noncommutative arithmetic–geometric mean inequality: conjectures, case studies, and consequences, in: Proceedings of the 25th Annual Conference on Learning Theory, Edinburgh, June 2012. – volume: 15 start-page: 573 year: 2002 end-page: 597 ident: b0300 article-title: The method of alternating projections and the method of subspace corrections in Hilbert space publication-title: J. Amer. Math. Soc. – volume: 420 start-page: 1 year: 1991 end-page: 43 ident: b0050 article-title: On a problem of Kadison and Singer publication-title: J. Reine Angew. Math. – reference: G.H. Golub, C.F. Van Loan, Matrix computations, Johns Hopkins Studies in the Mathematical Sciences, third ed., Johns Hopkins University Press, Baltimore, MD, 1996. – volume: 21 start-page: 1275 year: 1993 end-page: 1294 ident: b0055 article-title: Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix publication-title: Ann. Probab. – volume: 15 start-page: 262 year: 2009 end-page: 278 ident: b0250 article-title: A randomized Kaczmarz algorithm with exponential convergence publication-title: J. Fourier Anal. Appl. – reference: N. Srivastava, Spectral sparsification and restricted invertibility, Ph.D. dissertation, Yale University, New Haven, CT, 2010. – volume: 12 start-page: 389 year: 2012 end-page: 434 ident: b0275 article-title: User-friendly tail bounds for sums of random matrices publication-title: Found. Comput. Math. – reference: C.F. Gauss, Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Supplementum, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), 1995 (Transl. G.W. Stewart). – volume: 15 start-page: 437 year: 2009 end-page: 440 ident: b0245 article-title: Comments on the randomized Kaczmarz method publication-title: J. Fourier Anal. Appl. – reference: J.A. Tropp, Column subset selection, matrix factorization, and eigenvalue optimization, in: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, 2009, pp. 978–986. – reference: D. Needell, R. Ward, Two-subspace projection method for coherent overdetermined linear systems. – volume: 3 start-page: 115 year: 2011 end-page: 126 ident: b0270 article-title: Improved analysis of the subsampled randomized Hadamard transform publication-title: Adv. Adapt. Data Anal. – volume: 29 start-page: 471 year: 1970 end-page: 481 ident: b0125 article-title: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography publication-title: J. Theoret. Biol. – volume: 12 start-page: 135 year: 2004 end-page: 146 ident: b0215 article-title: A Kaczmarz–Kovarik algorithm for symmetric ill-conditioned matrices publication-title: An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. – reference: P. Youssef, A note on column subset selection. – reference: H.G. Feichtinger, T. Strohmer, A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices, in: SampTA ’95: 1995 Workshop on Sampling Theory and Applications, Jurmala, Latvia, September 1995, pp. 32–37. – reference: E. Liberty, Accelerated dense random projections, Ph.D. dissertation, Yale University, New Haven, CT, 2009. – volume: vol. 32 year: 2001 ident: b0185 article-title: The mathematics of computerized tomography publication-title: Classics in Applied Mathematics – reference: B. Kashin, L. Tzafriri, Some remarks on coordinate restriction of operators to coordinate subspaces, Institute of Mathematics Preprint 12, Hebrew University, Jerusalem, 1993–1994. – reference: C. Cenker, H.G. Feichtinger, M. Mayer, H. Steier, T. Strohmer, New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling, in: Proceedings of the SPIE: Visual Communications and Image Processing, 1992, pp. 299–310. – volume: 190 start-page: 83 year: 2012 end-page: 91 ident: b0240 article-title: An elementary proof of the restricted invertibility theorem publication-title: Israel J. Math. – reference: R. Aharoni, Y. Censor, Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, in: Proceedings of the Fourth Haifa Matrix Theory Conference (Haifa, 1988), vol. 120, 1989, pp. 165–175. – volume: 57 start-page: 137 year: 1987 end-page: 224 ident: b0045 article-title: Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis publication-title: Israel J. Math. – volume: 42 start-page: 1079 year: 1971 end-page: 1083 ident: b0150 article-title: A bound on tail probabilities for quadratic forms in independent random variables publication-title: Ann. Math. Statist. – volume: vol. 51 start-page: 148 year: 2006 end-page: 154 ident: b0290 article-title: Random sets of isomorphism of linear operators on Hilbert space publication-title: High Dimensional Probability – volume: 12 start-page: 600 year: 1993 end-page: 609 ident: b0135 article-title: Algebraic reconstruction techniques can be made computationally efficient publication-title: IEEE Trans. Medical Imaging – reference: , June 2012. – year: 2008 ident: b0060 article-title: Applied Iterative Methods – reference: P. Richtárik, M. Takáč, Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. – start-page: 1 year: 2012 end-page: 20 ident: b0080 article-title: Almost sure convergence of the Kaczmarz algorithm with random measurements publication-title: J. Fourier Anal. Appl. – volume: 47 start-page: 2845 year: 2001 end-page: 2862 ident: b0090 article-title: Uncertainty principles and ideal atomic decomposition publication-title: IEEE Trans. Inform. Theory – volume: 8 start-page: 9 year: 2001 end-page: 26 ident: b0210 article-title: A fast Kaczmarz–Kovarik algorithm for consistent least-squares problems publication-title: Korean J. Comput. Appl. Math. – volume: 15 start-page: 431 year: 2009 end-page: 436 ident: b0075 article-title: A note on the behavior of the randomized Kaczmarz algorithm of Strohmer and Vershynin [mr2500924] publication-title: J. Fourier Anal. Appl. – volume: 346 start-page: 1271 year: 2008 end-page: 1274 ident: b0255 article-title: Norms of random submatrices and sparse approximation publication-title: C. R. Math. Acad. Sci. Paris – volume: 103 start-page: 2032 year: 2006 end-page: 2039 ident: b0085 article-title: The Kadison–Singer problem in mathematics and engineering publication-title: Proc. Natl. Acad. Sci. USA – volume: 58 start-page: 163 year: 2011 end-page: 177 ident: b0105 article-title: Acceleration of randomized Kaczmarz method via the Johnson–Lindenstrauss lemma publication-title: Numer. Algorithms – volume: 11 start-page: 28 year: 1988 end-page: 48 ident: b0035 article-title: Matrix norm inequalities and the relative Dixmier property publication-title: Integral Equations Operator Theory – year: 1996 ident: b0040 article-title: Numerical Methods for Least Squares Problems – reference: A. Naor, Sparse quadratic forms and their geometric applications, Technical Report No. 1033, Séminaire Bourbaki, January 2011. – volume: 50 start-page: 395 year: 2010 end-page: 403 ident: b0190 article-title: Randomized Kaczmarz solver for noisy linear systems publication-title: BIT – volume: 35 start-page: 641 year: 2010 end-page: 654 ident: b0175 article-title: Randomized methods for linear constraints: convergence rates and conditioning publication-title: Math. Oper. Res. – volume: 122 start-page: 172 year: 1987 end-page: 186 ident: b0235 article-title: Incorporation of a priori moment information into signal recovery and synthesis problems publication-title: J. Math. Anal. Appl. – reference: , May 2012. – reference: S. Foucart, H. Rauhut, A Mathematical Introduction to Compressive Sensing, Birkha, Applied and Numerical Harmonic Analysis, in press. – volume: 81 start-page: 383 year: 1959 end-page: 400 ident: b0160 article-title: Extensions of pure states publication-title: Amer. J. Math. – volume: 185 start-page: 67 year: 2008 end-page: 82 ident: b0260 article-title: The random paving property for uniformly bounded matrices publication-title: Studia Math. – volume: 122 start-page: 253 year: 2001 end-page: 277 ident: b0285 article-title: John’s decompositions: selecting a large part publication-title: Israel J. Math. – reference: , April 2011. – volume: 29 start-page: 335 year: 1937 end-page: 357 ident: b0155 article-title: Angenäherte auflösung von systemen linearer gleichungen publication-title: Bull. Int. Acad. Polon. Sci. Lett. Ser. A – reference: , December 2012. – volume: 53 start-page: 217 year: 2011 end-page: 288 ident: b0140 article-title: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions publication-title: SIAM Rev. – volume: 59 start-page: 231 year: 1993 end-page: 247 ident: b0280 article-title: Dual coordinate ascent methods for non-strictly convex minimization publication-title: Math. Programming – reference: , April 2012. – volume: 38 start-page: 151 year: 1998 end-page: 176 ident: b0200 article-title: Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deficient least-squares problems publication-title: BIT – volume: 40 start-page: 37 year: 1981 end-page: 67 ident: b0095 article-title: Iterative algorithms for large partitioned linear systems, with applications to image reconstruction publication-title: Linear Algebra Appl. – volume: 25 start-page: 335 year: 2008 end-page: 366 ident: b0295 article-title: A fast randomized algorithm for the approximation of matrices publication-title: Appl. Comput. Harmon. Anal. – reference: A. Zouzias, N.M. Freris, Randomized extended Kaczmarz for solving least-squares. – volume: 82 start-page: 1479 year: 2012 end-page: 1487 ident: b0065 article-title: Invertibility of random submatrices via tail decoupling and a matrix Chernoff inequality publication-title: Statist. Probab. Lett. – volume: 39 start-page: 302 year: 2009 end-page: 322 ident: b0010 article-title: The fast Johnson–Lindenstrauss transform and approximate nearest neighbors publication-title: SIAM J. Comput. – reference: M. Benzi, Key moments in the history of numerical analysis, Presented at 2009 SIAM Applied Linear Algebra Conference, October 2009. – volume: 39 start-page: 323 year: 1999 end-page: 338 ident: b0205 article-title: Block-projections algorithms with blocks containing mutually orthogonal rows and columns publication-title: BIT – volume: 32 start-page: 1217 year: 2010 end-page: 1236 ident: b0015 article-title: Blendenpik: supercharging Lapack’s least-squares solver publication-title: SIAM J. Sci. Comput. – volume: 35 start-page: 1 year: 1980 end-page: 12 ident: b0100 article-title: Block-iterative methods for consistent and inconsistent linear equations publication-title: Numer. Math. – volume: 249 start-page: 303 year: 1979 end-page: 329 ident: b0020 article-title: Extensions, restrictions, and representations of states on publication-title: Trans. Amer. Math. Soc. – reference: C. Boutsidis, A. Gittens, Improved matrix algorithms via the Subsampled Randomized Hadamard Transform. – volume: 62 start-page: 1 year: 1978 end-page: 23 ident: b0145 article-title: The angles between the null spaces of X-rays publication-title: J. Math. Anal. Appl. – reference: P. Youssef, Restricted invertibility and the Banach–Mazur distance to the cube. – ident: 10.1016/j.laa.2012.12.022_b0305 – ident: 10.1016/j.laa.2012.12.022_b0310 doi: 10.1112/S0025579313000144 – volume: 15 start-page: 431 issue: 4 year: 2009 ident: 10.1016/j.laa.2012.12.022_b0075 article-title: A note on the behavior of the randomized Kaczmarz algorithm of Strohmer and Vershynin [mr2500924] publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-009-9077-x – volume: 47 start-page: 2845 issue: 7 year: 2001 ident: 10.1016/j.laa.2012.12.022_b0090 article-title: Uncertainty principles and ideal atomic decomposition publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.959265 – ident: 10.1016/j.laa.2012.12.022_b0195 doi: 10.5642/tspmcos.2012.01 – volume: 57 start-page: 137 issue: 2 year: 1987 ident: 10.1016/j.laa.2012.12.022_b0045 article-title: Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis publication-title: Israel J. Math. doi: 10.1007/BF02772174 – volume: vol. 32 year: 2001 ident: 10.1016/j.laa.2012.12.022_b0185 article-title: The mathematics of computerized tomography – volume: 122 start-page: 253 year: 2001 ident: 10.1016/j.laa.2012.12.022_b0285 article-title: John’s decompositions: selecting a large part publication-title: Israel J. Math. doi: 10.1007/BF02809903 – volume: 15 start-page: 573 issue: 3 year: 2002 ident: 10.1016/j.laa.2012.12.022_b0300 article-title: The method of alternating projections and the method of subspace corrections in Hilbert space publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-02-00398-3 – ident: 10.1016/j.laa.2012.12.022_b0170 – ident: 10.1016/j.laa.2012.12.022_b0115 – volume: 62 start-page: 1 issue: 1 year: 1978 ident: 10.1016/j.laa.2012.12.022_b0145 article-title: The angles between the null spaces of X-rays publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(78)90214-7 – volume: 29 start-page: 471 year: 1970 ident: 10.1016/j.laa.2012.12.022_b0125 article-title: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography publication-title: J. Theoret. Biol. doi: 10.1016/0022-5193(70)90109-8 – volume: 82 start-page: 1479 issue: 7 year: 2012 ident: 10.1016/j.laa.2012.12.022_b0065 article-title: Invertibility of random submatrices via tail decoupling and a matrix Chernoff inequality publication-title: Statist. Probab. Lett. doi: 10.1016/j.spl.2012.03.038 – volume: 8 start-page: 9 issue: 1 year: 2001 ident: 10.1016/j.laa.2012.12.022_b0210 article-title: A fast Kaczmarz–Kovarik algorithm for consistent least-squares problems publication-title: Korean J. Comput. Appl. Math. doi: 10.1007/BF03011619 – ident: 10.1016/j.laa.2012.12.022_b0220 – ident: 10.1016/j.laa.2012.12.022_b0025 – ident: 10.1016/j.laa.2012.12.022_b0030 doi: 10.1137/120874540 – ident: 10.1016/j.laa.2012.12.022_b0180 – volume: 35 start-page: 1 issue: 1 year: 1980 ident: 10.1016/j.laa.2012.12.022_b0100 article-title: Block-iterative methods for consistent and inconsistent linear equations publication-title: Numer. Math. doi: 10.1007/BF01396365 – ident: 10.1016/j.laa.2012.12.022_b0230 – volume: vol. 51 start-page: 148 year: 2006 ident: 10.1016/j.laa.2012.12.022_b0290 article-title: Random sets of isomorphism of linear operators on Hilbert space – volume: 42 start-page: 1079 year: 1971 ident: 10.1016/j.laa.2012.12.022_b0150 article-title: A bound on tail probabilities for quadratic forms in independent random variables publication-title: Ann. Math. Statist. doi: 10.1214/aoms/1177693335 – volume: 39 start-page: 323 issue: 2 year: 1999 ident: 10.1016/j.laa.2012.12.022_b0205 article-title: Block-projections algorithms with blocks containing mutually orthogonal rows and columns publication-title: BIT doi: 10.1023/A:1022398014630 – volume: 15 start-page: 262 issue: 2 year: 2009 ident: 10.1016/j.laa.2012.12.022_b0250 article-title: A randomized Kaczmarz algorithm with exponential convergence publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-008-9030-4 – volume: 3 start-page: 115 issue: 1–2 year: 2011 ident: 10.1016/j.laa.2012.12.022_b0270 article-title: Improved analysis of the subsampled randomized Hadamard transform publication-title: Adv. Adapt. Data Anal. doi: 10.1142/S1793536911000787 – volume: 12 start-page: 135 issue: 2 year: 2004 ident: 10.1016/j.laa.2012.12.022_b0215 article-title: A Kaczmarz–Kovarik algorithm for symmetric ill-conditioned matrices publication-title: An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. – volume: 103 start-page: 2032 issue: 7 year: 2006 ident: 10.1016/j.laa.2012.12.022_b0085 article-title: The Kadison–Singer problem in mathematics and engineering publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.0507888103 – volume: 249 start-page: 303 issue: 2 year: 1979 ident: 10.1016/j.laa.2012.12.022_b0020 article-title: Extensions, restrictions, and representations of states on C∗-algebras publication-title: Trans. Amer. Math. Soc. – volume: 58 start-page: 163 issue: 2 year: 2011 ident: 10.1016/j.laa.2012.12.022_b0105 article-title: Acceleration of randomized Kaczmarz method via the Johnson–Lindenstrauss lemma publication-title: Numer. Algorithms doi: 10.1007/s11075-011-9451-z – ident: 10.1016/j.laa.2012.12.022_b0005 doi: 10.1016/0024-3795(89)90375-3 – volume: 40 start-page: 37 year: 1981 ident: 10.1016/j.laa.2012.12.022_b0095 article-title: Iterative algorithms for large partitioned linear systems, with applications to image reconstruction publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(81)90139-7 – ident: 10.1016/j.laa.2012.12.022_b0110 – volume: 81 start-page: 383 year: 1959 ident: 10.1016/j.laa.2012.12.022_b0160 article-title: Extensions of pure states publication-title: Amer. J. Math. doi: 10.2307/2372748 – volume: 29 start-page: 335 year: 1937 ident: 10.1016/j.laa.2012.12.022_b0155 article-title: Angenäherte auflösung von systemen linearer gleichungen publication-title: Bull. Int. Acad. Polon. Sci. Lett. Ser. A – volume: 38 start-page: 151 issue: 1 year: 1998 ident: 10.1016/j.laa.2012.12.022_b0200 article-title: Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deficient least-squares problems publication-title: BIT doi: 10.1007/BF02510922 – ident: 10.1016/j.laa.2012.12.022_b0265 doi: 10.1137/1.9781611973068.106 – volume: 35 start-page: 641 issue: 3 year: 2010 ident: 10.1016/j.laa.2012.12.022_b0175 article-title: Randomized methods for linear constraints: convergence rates and conditioning publication-title: Math. Oper. Res. doi: 10.1287/moor.1100.0456 – volume: 12 start-page: 389 issue: 4 year: 2012 ident: 10.1016/j.laa.2012.12.022_b0275 article-title: User-friendly tail bounds for sums of random matrices publication-title: Found. Comput. Math. doi: 10.1007/s10208-011-9099-z – ident: 10.1016/j.laa.2012.12.022_b0225 doi: 10.1007/s10107-012-0614-z – year: 1996 ident: 10.1016/j.laa.2012.12.022_b0040 – ident: 10.1016/j.laa.2012.12.022_b0120 – volume: 53 start-page: 217 issue: 2 year: 2011 ident: 10.1016/j.laa.2012.12.022_b0140 article-title: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions publication-title: SIAM Rev. doi: 10.1137/090771806 – volume: 15 start-page: 437 issue: 4 year: 2009 ident: 10.1016/j.laa.2012.12.022_b0245 article-title: Comments on the randomized Kaczmarz method publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-009-9082-0 – volume: 11 start-page: 28 issue: 1 year: 1988 ident: 10.1016/j.laa.2012.12.022_b0035 article-title: Matrix norm inequalities and the relative Dixmier property publication-title: Integral Equations Operator Theory doi: 10.1007/BF01236652 – volume: 190 start-page: 83 year: 2012 ident: 10.1016/j.laa.2012.12.022_b0240 article-title: An elementary proof of the restricted invertibility theorem publication-title: Israel J. Math. doi: 10.1007/s11856-011-0194-2 – ident: 10.1016/j.laa.2012.12.022_b0130 – start-page: 1 year: 2012 ident: 10.1016/j.laa.2012.12.022_b0080 article-title: Almost sure convergence of the Kaczmarz algorithm with random measurements publication-title: J. Fourier Anal. Appl. – volume: 50 start-page: 395 issue: 2 year: 2010 ident: 10.1016/j.laa.2012.12.022_b0190 article-title: Randomized Kaczmarz solver for noisy linear systems publication-title: BIT doi: 10.1007/s10543-010-0265-5 – ident: 10.1016/j.laa.2012.12.022_b0165 – volume: 39 start-page: 302 issue: 1 year: 2009 ident: 10.1016/j.laa.2012.12.022_b0010 article-title: The fast Johnson–Lindenstrauss transform and approximate nearest neighbors publication-title: SIAM J. Comput. doi: 10.1137/060673096 – volume: 12 start-page: 600 issue: 3 year: 1993 ident: 10.1016/j.laa.2012.12.022_b0135 article-title: Algebraic reconstruction techniques can be made computationally efficient publication-title: IEEE Trans. Medical Imaging doi: 10.1109/42.241889 – volume: 21 start-page: 1275 issue: 3 year: 1993 ident: 10.1016/j.laa.2012.12.022_b0055 article-title: Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix publication-title: Ann. Probab. doi: 10.1214/aop/1176989118 – volume: 122 start-page: 172 issue: 1 year: 1987 ident: 10.1016/j.laa.2012.12.022_b0235 article-title: Incorporation of a priori moment information into signal recovery and synthesis problems publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(87)90352-0 – volume: 32 start-page: 1217 issue: 3 year: 2010 ident: 10.1016/j.laa.2012.12.022_b0015 article-title: Blendenpik: supercharging Lapack’s least-squares solver publication-title: SIAM J. Sci. Comput. doi: 10.1137/090767911 – volume: 346 start-page: 1271 issue: 23–24 year: 2008 ident: 10.1016/j.laa.2012.12.022_b0255 article-title: Norms of random submatrices and sparse approximation publication-title: C. R. Math. Acad. Sci. Paris doi: 10.1016/j.crma.2008.10.008 – ident: 10.1016/j.laa.2012.12.022_b0315 doi: 10.1137/120889897 – volume: 420 start-page: 1 year: 1991 ident: 10.1016/j.laa.2012.12.022_b0050 article-title: On a problem of Kadison and Singer publication-title: J. Reine Angew. Math. – ident: 10.1016/j.laa.2012.12.022_b0070 doi: 10.1117/12.131447 – year: 2008 ident: 10.1016/j.laa.2012.12.022_b0060 – volume: 25 start-page: 335 issue: 3 year: 2008 ident: 10.1016/j.laa.2012.12.022_b0295 article-title: A fast randomized algorithm for the approximation of matrices publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2007.12.002 – volume: 185 start-page: 67 issue: 1 year: 2008 ident: 10.1016/j.laa.2012.12.022_b0260 article-title: The random paving property for uniformly bounded matrices publication-title: Studia Math. doi: 10.4064/sm185-1-4 – volume: 59 start-page: 231 issue: 2, Ser. A year: 1993 ident: 10.1016/j.laa.2012.12.022_b0280 article-title: Dual coordinate ascent methods for non-strictly convex minimization publication-title: Math. Programming doi: 10.1007/BF01581245 |
| SSID | ssj0004702 |
| Score | 2.5306702 |
| Snippet | The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 199 |
| SubjectTerms | Algebraic reconstruction technique Block Kaczmarz Matrix paving Projections onto convex sets |
| Title | Paved with good intentions: Analysis of a randomized block Kaczmarz method |
| URI | https://dx.doi.org/10.1016/j.laa.2012.12.022 |
| Volume | 441 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELaqssCAeIryqDwwIYXaiZM4bKWi6kNUDFTqFvkVVGibqi0MHfjtnPMoIAEDUhZHd1L0xbnPse--Q-jSpYJ6mhkHuNh1WERsmxclHUo9AeHQsMRkap-DoDNkvZE_qqBWWQtj0yqL2J_H9CxaF3caBZqN-Xhsa3wzMT3fHshYWUxbwc5CO8uv3z_TPFhICsVw5ljr8mQzy_GaCCs9RN1sR9B1f-amL3zT3kO7xUIRN_Nn2UcVMztAO_cbldXlIeo9iDejsd1KxU9pqrHVfsiyF5c3uFQbwWmCBQZG0ul0vAZzCfT1gvtCradiscZ5C-kjNGzfPbY6TtEbwVEeIyvHV8DE3NOREMrjKuAicE3gJkDIIZERIYJwpmSSCEW1VvBZKuN6KoL_Fw0srb1jVJ2lM3OCsGBJAEzJpPAokzKUPldJoBX3ueSCJzVESlRiVQiH2_4Vk7jMEHuOAcjYAhnDBUDW0NXGZZ6rZvxlzEqo42-vPoao_rvb6f_cztA2jGzmjUP9c1RdLV7NBawrVrKeTZw62mp2-50BjLqj2w8Zd8zV |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LSsNAFL1oXagL8Yn1OQvdCNFkMkmnggtRS7W2uLDQXZxXpNo2YqtiF_6UP-idNPEB6kIQskpmQnJyuWcyc-ZcgC3qCc_XzDjIxdRhZdeWeVHS8TxfYDo0LDap22cjrDbZWStojcFrvhfGyiqz3D_K6Wm2zs7sZWju3bXbdo9vaqYX2AUZa4uZKStr5vkJ_9v6B6fH-JG3Ka2cXB5Vnay0gKN85g6cQCGRcV-XhVA-VyEXITUhjZHPSq4su65wOVMyjoXytFYY1cpQX5Vx-K-R5LSP9x2HCYbpwpZN2H350JWwkptZlDPHPl6-lJqKyjrCeh15NJ2CpPR7MvxEcJVZmMlGpuRw9PJzMGZ68zBdf7d17S_A2YV4NJrYuVtynSSaWLOJVC7Z3ye5vQlJYiIIUqBOuu0hNpfIl7ekJtSwK-6HZFSzehGa_4LYEhR6Sc8sAxEsDpGamRS-x6QsyYCrONSKB1xyweMiuDkqkcqcym3BjE6US9JuIgQyskBGeCCQRdh573I3sun4rTHLoY6-xFqENPJzt5W_dduEyepl_Tw6P23UVmEKr1jZj-MFa1AY3D-YdRzUDORGGkQErv47at8AmJ0Hkg |
| 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=Paved+with+good+intentions%3A+Analysis+of+a+randomized+block+Kaczmarz+method&rft.jtitle=Linear+algebra+and+its+applications&rft.au=Needell%2C+Deanna&rft.au=Tropp%2C+Joel+A.&rft.date=2014-01-15&rft.pub=Elsevier+Inc&rft.issn=0024-3795&rft.eissn=1873-1856&rft.volume=441&rft.spage=199&rft.epage=221&rft_id=info:doi/10.1016%2Fj.laa.2012.12.022&rft.externalDocID=S0024379513000098 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0024-3795&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0024-3795&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0024-3795&client=summon |