A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem

In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains a...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:SIAM journal on scientific and statistical computing Ročník 8; číslo 2; s. s139 - s154
Hlavní autori: Dongarra, J. J., Sorensen, D. C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia, PA Society for Industrial and Applied Mathematics 01.03.1987
Predmet:
Algorithms
Computational mathematics
Eigenvalues
Eigenvectors
Exact sciences and technology
Mathematics
Matrix
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Parallel algorithm
Mathematical matrix
Eigenvalue problem
Symmetric matrix
ISSN:0196-5204, 1064-8275, 2168-3417, 1095-7197
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains a number of active parallel processes that is greater than or equal to the initial number throughout the course of the computation. We give a new deflation technique which together with a robust root finding technique will assure computation of an eigensystem to full accuracy in the residuals and in the orthogonality of eigenvectors. A brief analysis of the numerical properties and sensitivity to round off error is presented to indicate where numerical difficulties may occur. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. Computational results are presented for several machines. These results are very encouraging with respect to both accuracy and speedup. A surprising result is that the parallel algorithm, even when run in serial mode, can be significantly faster than the previously best sequential algorithm on large problems, and is effective on moderate size problems when run in serial mode.
AbstractList In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains a number of active parallel processes that is greater than or equal to the initial number throughout the course of the computation. We give a new deflation technique which together with a robust root finding technique will assure computation of an eigensystem to full accuracy in the residuals and in the orthogonality of eigenvectors. A brief analysis of the numerical properties and sensitivity to round off error is presented to indicate where numerical difficulties may occur. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. Computational results are presented for several machines. These results are very encouraging with respect to both accuracy and speedup. A surprising result is that the parallel algorithm, even when run in serial mode, can be significantly faster than the previously best sequential algorithm on large problems, and is effective on moderate size problems when run in serial mode.
Author Sorensen, D. C.
Dongarra, J. J.
Author_xml – sequence: 1
  givenname: J. J.
  surname: Dongarra
  fullname: Dongarra, J. J.
– sequence: 2
  givenname: D. C.
  surname: Sorensen
  fullname: Sorensen, D. C.
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8120757$$DView record in Pascal Francis
BookMark eNpl0F1LwzAYBeAgE9ym-BeCCF5V37dfaa5kjE2FgQP1uqRpsmWkzUxaYf_eyoYXenVuHs6BMyGj1rWKkGuEe8SEPQCHArA4I-MY8yJKUmQjMgbkeZTFkF6QSQg7gAQzno7J44wue2sPdC28sFZZOrMb5023bah2nnZbRd8OTaM6byRdmI1qv4TtFV17V1nVXJJzLWxQV6ecko_l4n3-HK1en17ms1UkMUt4VAPwGpVMBZOxKuoUESpWCcQMQdUyUcA4EzrXLKsEpKiV5hWoPM25hEwkU3Jz7N1799mr0JU71_t2mCx5DEWR85gP6PaERJDCai9aaUK596YR_lAWGAPL2MDujkx6F4JX-lcglD8flqcPBxn9kdJ0ojOu7bww9p__BmEech4
CODEN SIJCD4
CitedBy_id crossref_primary_10_1177_109434209701100302
crossref_primary_10_1007_BF02196596
crossref_primary_10_1137_S0895479895288851
crossref_primary_10_1007_BF02142694
crossref_primary_10_1177_109434209200600103
crossref_primary_10_1137_S089547989122017X
crossref_primary_10_1016_0168_9274_93_90101_V
crossref_primary_10_1016_0021_9991_88_90167_2
crossref_primary_10_1016_j_compstruc_2018_04_007
crossref_primary_10_1016_j_amc_2004_01_026
crossref_primary_10_1016_j_laa_2007_05_008
crossref_primary_10_1137_15M1018812
crossref_primary_10_1137_0914046
crossref_primary_10_1007_BF00142664
crossref_primary_10_1061__ASCE_0733_9399_1999_125_5_587
crossref_primary_10_1016_j_camwa_2004_03_017
crossref_primary_10_1016_S0898_1221_03_90229_X
crossref_primary_10_1137_S0036144595288554
crossref_primary_10_1145_1268776_1268780
crossref_primary_10_1137_S0895479899359539
crossref_primary_10_1137_S1064827594273225
crossref_primary_10_1137_21M1438633
crossref_primary_10_1137_S0895479891196673
crossref_primary_10_1137_S0895479893252003
crossref_primary_10_1016_0024_3795_88_90309_6
crossref_primary_10_1016_j_amc_2023_128170
crossref_primary_10_1016_0167_8191_90_90147_2
crossref_primary_10_1016_0045_7949_94_90390_5
crossref_primary_10_1177_109434209300700402
crossref_primary_10_1016_j_neucom_2018_01_005
crossref_primary_10_1016_S0377_0427_97_00152_0
crossref_primary_10_1023_A_1019146505291
crossref_primary_10_1090_S0025_5718_1993_1164126_4
crossref_primary_10_1109_88_219856
crossref_primary_10_1016_0898_1221_93_90057_3
crossref_primary_10_1093_genetics_iyae143
crossref_primary_10_1016_0167_8191_92_90059_G
crossref_primary_10_1145_513001_513004
crossref_primary_10_1016_S0167_8191_99_00087_3
crossref_primary_10_1109_TNNLS_2019_2935455
crossref_primary_10_1137_0614016
crossref_primary_10_1016_j_amc_2004_11_008
crossref_primary_10_1016_j_laa_2012_01_031
crossref_primary_10_1080_00207169008803913
crossref_primary_10_1016_0743_7315_92_90066_V
crossref_primary_10_1007_BF02241709
crossref_primary_10_1016_j_jpdc_2007_10_001
crossref_primary_10_1137_120870785
crossref_primary_10_1016_0925_2312_94_00077_8
crossref_primary_10_1137_070708743
crossref_primary_10_2316_Journal_202_2004_4_204_0447
crossref_primary_10_1137_S1064827598336951
crossref_primary_10_1137_S089547989120195X
crossref_primary_10_1007_BF01165133
crossref_primary_10_1137_030601107
crossref_primary_10_1109_12_106219
crossref_primary_10_1016_j_enbuild_2023_113600
crossref_primary_10_1016_j_acha_2012_06_003
crossref_primary_10_1137_S1064827592228833
crossref_primary_10_1016_0377_0427_89_90366_X
crossref_primary_10_1016_S0167_8655_02_00214_3
crossref_primary_10_1137_0914078
crossref_primary_10_1137_100806783
crossref_primary_10_1137_0729015
crossref_primary_10_1137_S1064827596300681
crossref_primary_10_1016_0024_3795_93_90213_8
crossref_primary_10_1023_A_1021933127041
crossref_primary_10_1137_0613028
crossref_primary_10_1016_0377_0427_90_90006_L
crossref_primary_10_1002_cpe_4330030610
crossref_primary_10_1137_S1064827594269056
crossref_primary_10_1016_0167_8191_88_90108_1
crossref_primary_10_1016_0167_8191_94_90070_1
crossref_primary_10_1137_0728087
crossref_primary_10_1016_0377_0427_89_90367_1
crossref_primary_10_1016_j_amc_2003_07_009
crossref_primary_10_1017_S096249290000235X
crossref_primary_10_1007_BF01202143
crossref_primary_10_1016_0377_0427_94_00085_F
crossref_primary_10_1016_S0377_0427_97_82122_X
crossref_primary_10_1007_s11075_012_9579_5
crossref_primary_10_1137_110823699
crossref_primary_10_1137_0914008
crossref_primary_10_1016_0021_9991_90_90177_3
crossref_primary_10_1016_0898_1221_90_90004_4
crossref_primary_10_1016_j_laa_2013_10_007
crossref_primary_10_1137_060659454
crossref_primary_10_1137_0732072
crossref_primary_10_1137_S0895479893251472
crossref_primary_10_1016_0167_8191_93_90037_L
crossref_primary_10_1137_0915071
crossref_primary_10_1016_0377_0427_95_00124_7
crossref_primary_10_1137_21M139205X
crossref_primary_10_1137_S089547989223924X
crossref_primary_10_1007_BF01386438
crossref_primary_10_1007_s11128_019_2211_z
crossref_primary_10_1137_S0895479892241287
crossref_primary_10_1016_j_amc_2004_04_046
crossref_primary_10_1137_S1064827501399432
crossref_primary_10_1137_S0895479801383695
crossref_primary_10_1002_nme_6009
crossref_primary_10_1007_s00211_005_0595_4
crossref_primary_10_1145_131766_131770
crossref_primary_10_1137_1032002
crossref_primary_10_1145_44128_44130
crossref_primary_10_1080_10637199508915510
crossref_primary_10_1109_78_80968
crossref_primary_10_1007_BF02946602
crossref_primary_10_1002_jcc_540160108
crossref_primary_10_1109_TSP_2004_834212
crossref_primary_10_1016_j_laa_2015_09_025
crossref_primary_10_1137_0614042
crossref_primary_10_1016_S0377_0427_00_00413_1
crossref_primary_10_1002_cpe_4330030304
crossref_primary_10_1137_0727045
crossref_primary_10_1090_S0025_5718_1992_1151113_4
crossref_primary_10_1002_nla_1680020309
crossref_primary_10_1016_j_cam_2017_08_008
crossref_primary_10_1137_0609004
crossref_primary_10_1090_S0025_5718_98_00884_9
crossref_primary_10_1002_nla_1680020302
crossref_primary_10_1016_S0045_7949_96_00369_0
crossref_primary_10_1137_S0895479895282623
crossref_primary_10_1017_S0962492900002774
crossref_primary_10_1061__ASCE_0893_1321_1996_9_3_70
crossref_primary_10_1137_0914035
crossref_primary_10_1109_MCSE_2004_25
crossref_primary_10_1080_03081089008818000
Cites_doi 10.1007/3-540-07546-1
10.1007/BF01396012
10.1007/BF02169154
10.1007/BF02162161
10.1007/BF01396757
10.1109/MC.1984.1659186
10.1137/1015032
10.1007/BFb0067700
ContentType Journal Article
Copyright 1987 INIST-CNRS
[Copyright] © 1987 Society for Industrial and Applied Mathematics
Copyright_xml – notice: 1987 INIST-CNRS
– notice: [Copyright] © 1987 Society for Industrial and Applied Mathematics
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
DOI 10.1137/0908018
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 Global (Alumni Edition)
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 Edition)
Research Library (Alumni Edition)
ProQuest SciTech Premium Collection Technology Collection Materials Science & Engineering Database
ProQuest Central (Alumni Edition)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
Agricultural & Environmental Science Collection
ProQuest Central Essentials
ProQuest SciTech Premium Collection Natural Science Collection Biological Science Collection
ProQuest Central
Business Premium Collection
ProQuest Technology Collection
Natural Science Collection
ProQuest One Community College
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
ProQuest Biological Science Collection
ABI/INFORM Global
Agricultural Science Database
Computing Database
Military Database
Research Library
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
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)
DatabaseTitleList Agricultural Science Database
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Mathematics
EISSN 2168-3417
1095-7197
EndPage s154
ExternalDocumentID 2583236881
8120757
10_1137_0908018
GroupedDBID -~X
123
186
8FE
8FG
8G5
AAYXX
ABDPE
ABUWG
ACBEA
AFFNX
ALMA_UNASSIGNED_HOLDINGS
ARAPS
ATCPS
AZQEC
BBNVY
BENPR
BEZIV
BHPHI
BPHCQ
CITATION
CS3
D1I
DWQXO
FRNLG
GNUQQ
HCIFZ
H~9
K6V
L6V
M0C
M2O
P62
RJG
RNS
TN5
VOH
YNT
IQODW
3V.
4.4
7WY
7X2
7XB
7XC
88A
88I
88K
8AL
8CJ
8FH
8FK
8FL
ABJCF
ACGFO
ACGOD
ACIWK
ACPRK
ADBBV
AENEX
AFKRA
AFRAH
BGLVJ
CCPQU
CZ9
D0L
D1J
D1K
DU5
EBS
EJD
ESX
F5P
GUQSH
JQ2
K6-
K60
K6~
K7-
KB.
KC.
L.-
LK5
LK8
M0K
M0N
M1Q
M2P
M2T
M7P
M7R
M7S
MBDVC
P1Q
PATMY
PDBOC
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PROAC
PTHSS
PYCSY
Q9U
RSI
ID FETCH-LOGICAL-c1539-d009d1ec4a7c2e8d4110b7ba11510edc3e0797af6f75ba041fef9b0e6469c05a3
IEDL.DBID M1Q
ISSN 0196-5204
1064-8275
IngestDate Fri Jul 25 12:25:14 EDT 2025
Wed Apr 02 07:27:25 EDT 2025
Sat Nov 29 04:05:50 EST 2025
Tue Nov 18 21:51:51 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Parallel algorithm
Mathematical matrix
Eigenvalue problem
Symmetric matrix
Language English
License CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c1539-d009d1ec4a7c2e8d4110b7ba11510edc3e0797af6f75ba041fef9b0e6469c05a3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
PQID 920886929
PQPubID 666298
ParticipantIDs proquest_journals_920886929
pascalfrancis_primary_8120757
crossref_primary_10_1137_0908018
crossref_citationtrail_10_1137_0908018
PublicationCentury 1900
PublicationDate 19870301
PublicationDateYYYYMMDD 1987-03-01
PublicationDate_xml – month: 03
  year: 1987
  text: 19870301
  day: 01
PublicationDecade 1980
PublicationPlace Philadelphia, PA
PublicationPlace_xml – name: Philadelphia, PA
– name: Philadelphia
PublicationTitle SIAM journal on scientific and statistical computing
PublicationYear 1987
Publisher Society for Industrial and Applied Mathematics
Publisher_xml – name: Society for Industrial and Applied Mathematics
References R2
R10
R3
R4
R12
R11
R9
Wilkinson J. H. (R15) 1965
R1
Stewart G. W. (R14) 1973
References_xml – volume-title: Introduction to matrix computations
  year: 1973
  ident: R14
– ident: R12
  doi: 10.1007/3-540-07546-1
– ident: R2
  doi: 10.1007/BF01396012
– ident: R11
  doi: 10.1007/BF02169154
– ident: R10
  doi: 10.1007/BF02162161
– ident: R3
  doi: 10.1007/BF01396757
– ident: R1
  doi: 10.1109/MC.1984.1659186
– ident: R4
  doi: 10.1137/1015032
– volume-title: The algebraic eigenvalue problem
  year: 1965
  ident: R15
– ident: R9
  doi: 10.1007/BFb0067700
SSID ssj0031594
ssj0016492
Score 1.3204188
Snippet In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested...
SourceID proquest
pascalfrancis
crossref
SourceType Aggregation Database
Index Database
Enrichment Source
StartPage s139
SubjectTerms Algorithms
Computational mathematics
Eigenvalues
Eigenvectors
Exact sciences and technology
Mathematics
Matrix
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Title A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
URI https://www.proquest.com/docview/920886929
Volume 8
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: Agricultural Science Database
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: M0K
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/agriculturejournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Biological Science Database (ProQuest)
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: M7P
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/biologicalscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: K7-
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: M7S
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Environmental Science Database
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: PATMY
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/environmentalscience
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Materials Science Database
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: KB.
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/materialsscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Military Database (ProQuest)
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: M1Q
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/military
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest ABI/INFORM Collection
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20131231
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: 7WY
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/abicomplete
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest ABI/INFORM Global
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 19921231
  omitProxy: false
  ssIdentifier: ssj0031594
  issn: 0196-5204
  databaseCode: M0C
  dateStart: 19800101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/abiglobal
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest advanced technologies & aerospace journals
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 19921231
  omitProxy: false
  ssIdentifier: ssj0031594
  issn: 0196-5204
  databaseCode: P5Z
  dateStart: 19800101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 19921231
  omitProxy: false
  ssIdentifier: ssj0031594
  issn: 0196-5204
  databaseCode: BENPR
  dateStart: 19800101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20131231
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  databaseCode: BENPR
  dateStart: 19800301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Research Library
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 19921231
  omitProxy: false
  ssIdentifier: ssj0031594
  issn: 0196-5204
  databaseCode: M2O
  dateStart: 19800101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/pqrl
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Science Database (ProQuest)
  customDbUrl:
  eissn: 2168-3417
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0016492
  issn: 0196-5204
  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/eLvHCXMwpV1Nb9QwEB3RlgOoolCK2JaufEDcDM6XHZ-qttoKqdol0CIKlyixHUDqbrebbaX--8443ghUiQuXUaKMosjjGb_xOPMA3qYmydCfFScea56mNuF5ZjOuY6r5NNQRpfFkE2oyyS8udBHO5rThWOUqJvpAba8M7ZF_0DH6g8TF_GB-zYk0ioqrgUFjDTYQJ2tqnT-OPvdFBJnqrtgpU57HKuv-mY0iaumjESkR0ccfi9HmvGpxXJqO0OJBbPYLzsnWf37qc3gWkCY77KbGC3jkZtuwFVAnCz7dbsPTcd-5tX0JB4eMstI7VlQLolnBF1z-xLcvf00Z4luGquzsbjolIi7DRtTLk_qFO1Z0zDQ78PVkdH78kQeSBW4w2GluEWTZyJm0UiZ2uU0RD9SqrhApRsJZkzihtKoa2aisrkQaNa7RtXAS82ojsip5Beuzq5l7DczaRtYYQWopKsxqrDZNLiSCAhcbIbUcwLvVaJcmdCAnIozL0mciiSqDWQbAesV513Tjocr-X-bq9RCwIApSA9hb2aYMXtmWvWF2__l0D57QVkx30uwNrC8XN24fHpvb5e92MYQ19e37EDaORpPiC96dKk7y6D3KsTj28nToZyLJ-JOXhZfnJJW_Vmcoi-zHPdhV5JE
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LSxxBEC6MBmIQTYwh6yPpQ5Jb4zx6uqcPIuIDZXVZiAFvk5l-JAF33exsEvZH5T9aNS8igjcPnqdo6Omvqr7qR30AH4WJE_RnxUnHmgthY54mNuE6ojMfTx1RfCU2oQaD9OpKDxfgX_sWhq5VtjGxCtT2xtAe-a6O0B8kJvP9yS9OolF0uNoqaNSo6Lv5X6zYyr2zI1zeT1F0cnx5eMobUQFu0Lk1t0gqbOiMyJWJXGoF5r9CFTkyozBw1sQuUFrlXnqVFHkgQu-8LgInsY40QZLHOO4zWBJxqsit-op3hxZS6PpwVQqeRiqp3-iGIbUQ0sjMSFjkv-S3MslLXAdfC2jcywVVgjtZe2K_5hWsNkyaHdTQfw0LbrwOaw2rZk3MKtfh5UXXmbZ8A_sHjKruORvmU5KRwQGuv-NsZj9GDPk7Q1P2ZT4akdCYYcfUq5T6oTs2rJV3NuDro0zqLSyOb8buHTBrvSwwQhYyyLFqs9r4NJBIelxkAqllDz63q5uZpsM6CX1cZ1WlFausgUEPWGc4qZuK3DfZuQOPzg4JGbI81YOtFgtZE3XKrAPC5oNfP8CL08uL8-z8bNDfgmXadqpv1W3D4mz62-3Ac_Nn9rOcvq_wzeDbY6PmFuseNcs
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=A+Fully+Parallel+Algorithm+for+the+Symmetric+Eigenvalue+Problem&rft.jtitle=SIAM+journal+on+scientific+and+statistical+computing&rft.au=Dongarra%2C+J.+J.&rft.au=Sorensen%2C+D.+C.&rft.date=1987-03-01&rft.issn=0196-5204&rft.eissn=2168-3417&rft.volume=8&rft.issue=2&rft.spage=s139&rft.epage=s154&rft_id=info:doi/10.1137%2F0908018&rft.externalDBID=n%2Fa&rft.externalDocID=10_1137_0908018
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0196-5204&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0196-5204&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0196-5204&client=summon