Fast and processor efficient parallel matrix multiplication algorithms on a linear array with a reconfigurable pipelined bus system
We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independen...
Saved in:
| Published in | IEEE transactions on parallel and distributed systems Vol. 9; no. 8; pp. 705 - 720 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.08.1998
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1045-9219 |
| DOI | 10.1109/71.706044 |
Cover
| Abstract | We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM/sub 1/, MM/sub 2/, MM/sub 3/, and compound algorithms C/sub 1/(/spl epsiv/)and C/sub 2/(/spl delta/). Algorithm C/sub 1/(/spl epsiv/) has adjustable time complexity in sublinear level. Algorithm C/sub 2/(/spl delta/) implies that it is feasible to achieve sublogarithmic time using /spl sigma/(N/sup 3/) processors for matrix multiplication on a realistic system. Algorithms MM/sub 3/, C/sub 1/(/spl epsiv/), and C/sub 2/(/spl delta/) all have o(/spl Nscr//sup 3/) cost and, hence, are very processor efficient. Algorithms MM/sub 1/, MM/sub 3/, and C/sub 1/(/spl epsiv/) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM/sub 2/ and C/sub 2/(/spl delta/) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM/sub 2/ and C/sub 2/(/spl delta/) to unbounded integers and reals are also discussed. |
|---|---|
| AbstractList | We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows: We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model, namely, MM sub(1), MM sub(2), MM sub(3), and compound algorithms C sub(1)( epsilon ) and C sub(2)( delta ). Algorithm C sub(1)( epsilon ) has adjustable time complexity in sublinear level. Algorithm C sub(2)( delta ) implies that it is feasible to achieve sublogarithmic time using o(N super(3)) processors for matrix multiplication on a realistic system. Algorithms MM sub(3), C sub(1)( epsilon ), and C sub(2)( delta ) all have o(N super(3)) cost and, hence, are very processor efficient. Algorithms MM sub(1), MM sub(3), and C sub(1)( epsilon ) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM sub(2) and C sub(2)( delta ) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM sub(2) and C sub(2)( delta ) to unbounded integers and reals are also discussed. We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM(1), MM (2), MM(3), and compound algorithms C(1)(epsilon)and C(2)(delta). Algorithm C(1)(epsilon) has adjustable time complexity in sublinear level. Algorithm C(2)(delta) implies that it is feasible to achieve sublogarithmic time using sigma(N(3)) processors for matrix multiplication on a realistic system. Algorithms MM(3), C(1)(epsilon), and C(2)(delta) all have o( (3)) cost and, hence, are very processor efficient. Algorithms MM(1), MM(3), and C(1)(epsilon) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM(2) and C(2)(delta) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM (2) and C(2)(delta) to unbounded integers and reals are also discussed We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM/sub 1/, MM/sub 2/, MM/sub 3/, and compound algorithms C/sub 1/(/spl epsiv/)and C/sub 2/(/spl delta/). Algorithm C/sub 1/(/spl epsiv/) has adjustable time complexity in sublinear level. Algorithm C/sub 2/(/spl delta/) implies that it is feasible to achieve sublogarithmic time using /spl sigma/(N/sup 3/) processors for matrix multiplication on a realistic system. Algorithms MM/sub 3/, C/sub 1/(/spl epsiv/), and C/sub 2/(/spl delta/) all have o(/spl Nscr//sup 3/) cost and, hence, are very processor efficient. Algorithms MM/sub 1/, MM/sub 3/, and C/sub 1/(/spl epsiv/) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM/sub 2/ and C/sub 2/(/spl delta/) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM/sub 2/ and C/sub 2/(/spl delta/) to unbounded integers and reals are also discussed. |
| Author | Si Qing Zheng Keqin Li Yi Pan |
| Author_xml | – sequence: 1 givenname: Keqin surname: Li fullname: Li, Keqin – sequence: 2 givenname: Yi surname: Pan fullname: Pan, Yi – sequence: 3 givenname: Si surname: Zheng middlename: Qing fullname: Zheng, Si Qing |
| BookMark | eNqFkb1PwzAQxT0UibYwsDJ5QmJIa-fDSUZUUUCqxAJzdHHOxcj5wHYEnfnHSUjFgJCYTnfv9066ewsya9oGCbngbMU5y9cpX6VMsDiekTlncRLkIc9PycK5V8Z4nLB4Tj634DyFpqKdbSU611qKSmmpsfG0AwvGoKE1eKs_aN0brzujJXjdNhTMvrXav9SOjh01ukGwFKyFA30fhGFmUbaN0vveQmmQdrrDEato2TvqDs5jfUZOFBiH58e6JM_b26fNfbB7vHvY3OwCGbHMBxEwJpUAoSrGc4ZJlSkRlZXkMk4q5EKkqVIJj7K8ikLFmJLxAOciDLGENIyW5GraO5z61qPzRa2dRGOgwbZ3RZiFuYh48j-YJhGPxbhxPYHSts5ZVIXU_vs33oI2BWfFmESR8mJKYnBc_3J0VtdgD3-ylxOrEfGHO4pfMayX5A |
| CODEN | ITDSEO |
| CitedBy_id | crossref_primary_10_1109_ACCESS_2022_3185133 crossref_primary_10_1016_j_compeleceng_2008_11_020 crossref_primary_10_1109_TIP_2012_2186308 crossref_primary_10_1006_jpdc_2001_1768 crossref_primary_10_1109_TPDS_2002_1058096 crossref_primary_10_1006_jpdc_2001_1726 crossref_primary_10_1016_j_imavis_2007_08_016 crossref_primary_10_1016_j_jpdc_2007_06_001 crossref_primary_10_1108_03321640210423298 crossref_primary_10_1109_TC_2002_1009153 crossref_primary_10_1016_j_physa_2014_04_013 crossref_primary_10_1006_jpdc_2000_1643 crossref_primary_10_1080_17445760601125434 crossref_primary_10_1006_jpdc_2000_1644 crossref_primary_10_1109_TPDS_2005_33 crossref_primary_10_1016_j_camwa_2003_06_009 crossref_primary_10_1016_j_parco_2008_10_003 crossref_primary_10_1109_TSMCB_2003_817062 crossref_primary_10_1109_71_993203 crossref_primary_10_1006_jpdc_2001_1821 crossref_primary_10_1080_10637190410001700604 crossref_primary_10_1016_S0262_8856_00_00044_5 crossref_primary_10_1006_jpdc_1999_1569 crossref_primary_10_1016_j_jpdc_2004_01_002 crossref_primary_10_1109_TPDS_2003_1239867 crossref_primary_10_3182_20130925_2_DE_4044_00021 crossref_primary_10_1109_TPDS_2007_1027 crossref_primary_10_1049_iet_cds_2013_0117 crossref_primary_10_1109_71_970563 crossref_primary_10_1016_S0167_8191_99_00126_X crossref_primary_10_1109_TSMCB_2003_817102 crossref_primary_10_1007_s11227_009_0319_0 crossref_primary_10_1109_TVLSI_2006_874302 crossref_primary_10_1016_S0031_3203_00_00100_X crossref_primary_10_1109_12_926164 crossref_primary_10_1080_1063719031000104996 crossref_primary_10_1007_s11265_020_01582_7 crossref_primary_10_1016_S0167_8191_02_00164_3 crossref_primary_10_1080_17445760500033309 crossref_primary_10_1109_71_862204 |
| Cites_doi | 10.1109/71.342133 10.1006/jnca.1996.0016 10.1117/12.56031 10.1117/1.601593 10.1007/978-1-4612-0265-3 10.1049/ip-cdt:19951621 10.1109/12.223677 10.1117/1.601494 10.1109/ISPAN.1997.645135 10.1109/MC.1987.1663446 10.1016/0020-0190(93)90233-Y 10.1023/A:1007922924139 10.1109/71.642947 10.1109/12.166601 10.1364/AO.29.002024 10.1109/MPPOI.1994.336629 10.1007/BF02165411 10.1109/40.76620 10.1016/S0167-739X(97)00013-7 10.1137/0210049 10.1016/0743-7315(91)90130-2 10.1080/10637199608915554 10.1109/12.277290 10.1007/978-1-4615-5611-4_34 10.1017/CBO9781107325708 10.1016/S0747-7171(08)80013-2 10.1145/22145.22161 10.1109/TC.1984.1676405 |
| ContentType | Journal Article |
| DBID | RIA RIE AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/71.706044 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EndPage | 720 |
| ExternalDocumentID | 10_1109_71_706044 706044 |
| GroupedDBID | --Z -~X .DC 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD HZ~ H~9 ICLAB IEDLZ IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNI RNS RZB TN5 TWZ UHB VH1 AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c308t-3a00cf6a6fd0190e5d8f63bdc1c45de16677ff51389d32f00fc4a6f9622eba723 |
| IEDL.DBID | RIE |
| ISSN | 1045-9219 |
| IngestDate | Sat Sep 27 23:44:31 EDT 2025 Thu Oct 02 03:46:07 EDT 2025 Thu Apr 24 23:05:19 EDT 2025 Wed Oct 01 02:59:01 EDT 2025 Wed Aug 27 02:52:20 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c308t-3a00cf6a6fd0190e5d8f63bdc1c45de16677ff51389d32f00fc4a6f9622eba723 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 27531462 |
| PQPubID | 23500 |
| PageCount | 16 |
| ParticipantIDs | crossref_citationtrail_10_1109_71_706044 proquest_miscellaneous_27531462 proquest_miscellaneous_28296315 ieee_primary_706044 crossref_primary_10_1109_71_706044 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 1900 |
| PublicationDate | 1998-08-01 |
| PublicationDateYYYYMMDD | 1998-08-01 |
| PublicationDate_xml | – month: 08 year: 1998 text: 1998-08-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationTitle | IEEE transactions on parallel and distributed systems |
| PublicationTitleAbbrev | TPDS |
| PublicationYear | 1998 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| References | leighton (bibl070520) 1992 bibl07055 bibl07056 bibl07059 akl (bibl07052) 1997 bibl070515 li (bibl070525) 1998 qiao (bibl070543) 1995 bibl07053 bibl07054 horng (bibl070517) 1995 bibl070522 bibl070521 bibl070524 trahan (bibl070548) 1997 bibl070527 (bibl070526) 1998 bibl070529 bibl070530 bibl070533 tocci (bibl070547) 1994 bibl070532 zheng (bibl070550) 1997; 36 pan (bibl070535) 1996 bibl070534 li (bibl070523) 1997 aho (bibl07051) 1974 pavel (bibl070542) 1996 bibl070536 bibl070539 bibl070538 dowd (bibl070513) 1992; 41 bibl070541 trahan (bibl070549) 0 bibl070544 bibl070546 chandra (bibl07058) 1979 bibl070545 guo (bibl070514) 1992 hamdi (bibl070516) 1995; 142 kumar (bibl070519) 1994 (bibl070518) 1985 pan (bibl070531) 1992 cannon (bibl07057) 1969 bibl070511 bibl070510 pavel (bibl070540) 1996 bibl070512 li (bibl070528) 1996 pan (bibl070537) 1993 |
| References_xml | – year: 1992 ident: bibl070520 publication-title: Introduction to Parallel Algorithms and Architectures Arrays Trees Hypercubes – ident: bibl070510 doi: 10.1109/71.342133 – ident: bibl070533 doi: 10.1006/jnca.1996.0016 – year: 1969 ident: bibl07057 article-title: a cellular computer to implement the kalman filter algorithm publication-title: "A Cellular Computer to Implement the Kalman Filter Algorithm " – ident: bibl07053 doi: 10.1117/12.56031 – volume: 36 start-page: 3,392 year: 1997 ident: bibl070550 article-title: pipelined asynchronous time-division multiplexing optical bus publication-title: Optical Eng doi: 10.1117/1.601593 – ident: bibl07054 doi: 10.1007/978-1-4612-0265-3 – volume: 142 start-page: 87 year: 1995 ident: bibl070516 article-title: efficient parallel algorithms on optically interconnected arrays of processors publication-title: Computers and Digital Techniques IEE Proceedings- doi: 10.1049/ip-cdt:19951621 – ident: bibl070544 doi: 10.1109/12.223677 – ident: bibl070527 doi: 10.1117/1.601494 – ident: bibl070536 doi: 10.1109/ISPAN.1997.645135 – year: 1979 ident: bibl07058 article-title: maximal parallelism in matrix multiplication – ident: bibl07059 doi: 10.1109/MC.1987.1663446 – ident: bibl070539 doi: 10.1016/0020-0190(93)90233-Y – year: 1974 ident: bibl07051 publication-title: The Design and Analysis of Computer Algorithms – ident: bibl070522 doi: 10.1023/A:1007922924139 – year: 1994 ident: bibl070547 publication-title: Optical Interconnection?Foundations and Applications – start-page: 621 year: 1993 ident: bibl070537 article-title: parallel solution of sparse linear and path systems publication-title: Synthesis of Parallel Algorithms – year: 1997 ident: bibl07052 publication-title: Parallel Computation Models and Methods – start-page: 1,443 year: 1996 ident: bibl070542 article-title: on the power of arrays with reconfigurable optical buses publication-title: Proc Int l Conf Parallel and Distributed Processing Techniques and Applications – ident: bibl070545 doi: 10.1109/71.642947 – year: 0 ident: bibl070549 article-title: scalable algorithms and simulation results on a linear array with a reconfigurable pipelined bus system – volume: 41 start-page: 1,223 year: 1992 ident: bibl070513 article-title: wavelength division multiple access channel hypercube processor interconnection publication-title: IEEE Trans Computes doi: 10.1109/12.166601 – start-page: 1,431 year: 1996 ident: bibl070535 article-title: linear array with a reconfigurable pipelined bus system-concepts and applications publication-title: Information Sciences?An Int l J – ident: bibl070521 doi: 10.1364/AO.29.002024 – start-page: 366 year: 1995 ident: bibl070517 article-title: prefix computation and some related applications on mesh connected computers with hyperbus broadcasting publication-title: Proc Int l Conf Computing and Information – ident: bibl070532 doi: 10.1109/MPPOI.1994.336629 – start-page: 69 year: 1996 ident: bibl070528 article-title: parallel selection on a pipelined tdm optical buses publication-title: Proc Int l Conf Parallel and Distributed Computing Systems – ident: bibl070546 doi: 10.1007/BF02165411 – year: 1994 ident: bibl070519 publication-title: Introduction to Parallel Computing Design and Analysis of Algorithms – ident: bibl070529 doi: 10.1109/40.76620 – ident: bibl070534 doi: 10.1016/S0167-739X(97)00013-7 – year: 1998 ident: bibl070526 publication-title: Parallel Computing Using Optical Interconnections – start-page: 590 year: 1997 ident: bibl070523 article-title: simulation of parallel random access machines on a linear array with a reconfigurable pipelined bus system publication-title: Proc Int l Conf Parallel and Distributed Processing Techniques and Applications – ident: bibl070512 doi: 10.1137/0210049 – ident: bibl070515 doi: 10.1016/0743-7315(91)90130-2 – start-page: 273 year: 1995 ident: bibl070543 article-title: efficient matrix operations in a reconfigurable array with spanning optical buses publication-title: Proc Fifth Symp Frontiers of Parallel Computation – ident: bibl070541 doi: 10.1080/10637199608915554 – ident: bibl070530 doi: 10.1109/12.277290 – ident: bibl070524 doi: 10.1007/978-1-4615-5611-4_34 – ident: bibl07056 doi: 10.1017/CBO9781107325708 – year: 1985 ident: bibl070518 publication-title: Standard 754 Order No CN-953 – year: 1998 ident: bibl070525 article-title: scalable parallel matrix multiplication using reconfigurable pipelined optical bus systems publication-title: Proc 10th Int l Conf Parallel and Distributed Computing and Systems – start-page: 161 year: 1992 ident: bibl070531 article-title: hough transform on arrays with an optical bus publication-title: Proc Fifth Int l Conf Parallel and Distributed Computing and Systems – start-page: 289 year: 1992 ident: bibl070514 article-title: sorting on array processors with pipelined buses publication-title: Proc Int l Conf Parallel Processing – start-page: 564 year: 1997 ident: bibl070548 article-title: scalable basic algorithms on a linear array with a reconfigurable pipelined bus system publication-title: Proc 10th Int l Conf Parallel and Distributed Computing Systems – ident: bibl070511 doi: 10.1016/S0747-7171(08)80013-2 – ident: bibl070538 doi: 10.1145/22145.22161 – ident: bibl07055 doi: 10.1109/TC.1984.1676405 – year: 1996 ident: bibl070540 article-title: computation and communication aspects of arrays with optical pipelined buses publication-title: "Computation and Communication Aspects of Arrays With Optical Pipelined Buses " |
| SSID | ssj0014504 |
| Score | 1.8139627 |
| Snippet | We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 705 |
| SubjectTerms | Concurrent computing Costs Eigenvalues and eigenfunctions Graph theory Optical arrays Parallel algorithms Parallel processing Polynomials Power engineering and energy Tree graphs |
| Title | Fast and processor efficient parallel matrix multiplication algorithms on a linear array with a reconfigurable pipelined bus system |
| URI | https://ieeexplore.ieee.org/document/706044 https://www.proquest.com/docview/27531462 https://www.proquest.com/docview/28296315 |
| Volume | 9 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) issn: 1045-9219 databaseCode: RIE dateStart: 19900101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://ieeexplore.ieee.org/ omitProxy: false ssIdentifier: ssj0014504 providerName: IEEE |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT9wwELaAEz2UsrQq0MII9cAlS5yHkxwR6gohwQkkbpGfdNWQrPKQoNf-cTx2dlUeqrgl0cSK4rHH8_i-IeRHYlKWccqs8oY8sLsfD4SSLKCKMi5ia2MMxjsur9j5TXJxm96OPNsOC6O1dsVneoqXLpevGjlgqOzEMb0k62Q9y5mHaq0SBknqOgVa5yINCrsKRxIhGhYnGZ36F5-ZHtdL5dUG7KzKbMvDtTtHRojFJL-nQy-m8s8LqsZ3fvAn8nE8XcKpV4dtsqbrCdladm6AcSFPyId_aAh3yN8Z73rgtYKFhw00LWhHLWFHByQHrypdwT2y-T_AWII4xvqAV3dNO-9_3XeAd4DHVt4Cb1v-CBjltc-c123md0OLQC1YzBeIgtcKxNCB55L-TG5mP6_PzoOxOUMg4zDvg5iHoTSMM6MQjq5TlRsW23mmMkmVpoxlmTEp5kFVHJkwNDKxwgWLIi14FsVfyEbd1PorAesCaSTBKURiElPYM78Ls-QmziIlhdglx8t5K-XIXI4NNKrSeTBhUWa09L96lxytRBeeruMtoQlO1Upg-fRwqQulXWKYN-G1boaujKxLZw1K9B-JPLIbGU333hx5n2x6JCOWDX4jG3076O_2KNOLA6fETztP9L4 |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1Lb9QwELagHIADhQVEeXWEOHDJNk5sZ3NEiNUCbU-t1FvkZ1mRJqs8JODKH8djZ1c8KsQtiSZWFI89nsf3DSGvmeOikFR45U1l4nc_mSijRUINFVLl3sY4jHecnIrVOft4wS8mnu2AhbHWhuIzO8fLkMs3rR4xVHYUmF7YTXKLM8Z4BGvtUgaMh16B3r3gSenX4UQjRNPyqKDz-Opvxid0U_lrCw52ZbkfAdt9oCPEcpIv83FQc_39D7LG__zk--TedL6Et1EhHpAbtpmR_W3vBpiW8ozc_YWI8CH5sZT9ALIxsInAgbYDG8gl_OiA9OB1bWu4Qj7_rzAVIU7RPpD1Zduth89XPeAd4MFVdiC7Tn4DjPP6Z8HvduvLsUOoFmzWG8TBWwNq7CGyST8i58v3Z-9WydSeIdF5uhiSXKapdkIKZxCQbrlZOJH7maaacWOpEEXhHMdMqMkzl6ZOMy9ciiyzShZZ_pjsNW1jnxDwTpBFGpxSMcdc6U_9IdCycHmRGa3UAXmznbdKT9zl2EKjroIPk5ZVQav4qw_Iq53oJhJ2XCc0w6naCWyfHm51ofKLDDMnsrHt2FeZd-q8Scn-IbHI_FZG-dNrRz4kt1dnJ8fV8YfTT8_InYhrxCLC52Rv6Eb7wh9sBvUyKPRPJsz4Cw |
| 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=Fast+and+processor+efficient+parallel+matrix+multiplication+algorithms+on+a+linear+array+with+a+reconfigurable+pipelined+bus+system&rft.jtitle=IEEE+transactions+on+parallel+and+distributed+systems&rft.au=Keqin+Li&rft.au=Yi+Pan&rft.au=Si+Qing+Zheng&rft.date=1998-08-01&rft.issn=1045-9219&rft.volume=9&rft.issue=8&rft.spage=705&rft.epage=720&rft_id=info:doi/10.1109%2F71.706044&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_71_706044 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1045-9219&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1045-9219&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1045-9219&client=summon |