Systolic givens factorization of dense rectangular matrices
Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The...
Saved in:
| Published in: | International journal of computer mathematics Vol. 25; no. 3-4; pp. 287 - 298 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Abingdon
Gordon and Breach Science Publishers
01.01.1988
Taylor and Francis Taylor & Francis |
| Subjects: | |
| ISSN: | 0020-7160, 1029-0265 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The pipelined version of the new algorithm leads to a systolic implementation whose area-time performances overcome those of the arrays of Bojanczyk, Brent and Kung [1] and Gentleman and Kung [5]. |
|---|---|
| AbstractList | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The pipelined version of the new algorithm leads to a systolic implementation whose area-time performances overcome those of the arrays of Bojanczyk, Brent and Kung [1] and Gentleman and Kung [5]. |
| Author | Robert, Yves Cosnard, Michel |
| Author_xml | – sequence: 1 givenname: Michel surname: Cosnard fullname: Cosnard, Michel organization: CNRS, Laboratoire TIM3 , Institut National Polytechnique de Grenoble – sequence: 2 givenname: Yves surname: Robert fullname: Robert, Yves organization: Ecole Normale Supérieure de Lyon |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7211088$$DView record in Pascal Francis https://inria.hal.science/hal-00857004$$DView record in HAL |
| BookMark | eNp9kMFKAzEQhoNUsK0-gLc9ePGwOtlskyx6kaJWKHhQz2GaTWpkuylJrNSnd2utB0VhYGDyfUPmH5Be61tDyDGFMwoSzgEKEJRLCV0xLso90qdQVDkUfNQj_c173gFwQAYxvgCArATvk4uHdUy-cTqbu5VpY2ZRJx_cOybn28zbrO6mJgtGJ2znrw2GbIEpOG3iIdm32ERz9NWH5Onm-nE8yaf3t3fjq2muGacpl1UhZ7SsGKupNWxEQRs0VhhuhJQjAzNuaaklhdqYcqY5gOBQIWO2KGtq2JCcbvc-Y6OWwS0wrJVHpyZXU7WZdceMBEC5oh17smWXGDU2NmCrXfy2REG7uGSHiS2mg48xGKu0S58np4CuURTUJlb1K9bOpD_M3e7_nMut41rrwwLffGhqlXDd-LD7Iftb_wC-h4y9 |
| CODEN | IJCMAT |
| CitedBy_id | crossref_primary_10_1016_0167_8191_89_90083_5 crossref_primary_10_1016_0743_7315_91_90029_9 crossref_primary_10_1016_0167_8191_90_90044_A |
| Cites_doi | 10.1117/12.932507 10.1137/1020096 10.1109/PROC.1966.5273 10.1145/6490.214102 10.1016/0024-3795(80)90156-1 10.1007/BF01389871 10.1007/BF01389639 10.1145/322047.322054 10.1145/322358.322366 10.1109/MC.1982.1653825 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 1988 1989 INIST-CNRS Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 1988 – notice: 1989 INIST-CNRS – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION IQODW 1XC |
| DOI | 10.1080/00207168808803674 |
| DatabaseName | CrossRef Pascal-Francis Hyper Article en Ligne (HAL) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science Applied Sciences |
| EISSN | 1029-0265 |
| EndPage | 298 |
| ExternalDocumentID | oai:HAL:hal-00857004v1 7211088 10_1080_00207168808803674 8803674 |
| GroupedDBID | -~X 07G 0R~ 1TA 4.4 5GY 5VS AAIKQ AAKBW AAYJJ ABEFU ABJNI ABUFD ACGEE ACGEJ ACGFS ACGOD ACIWK ACNCT ADCVX ADXPE AENEX AEPSL AEUMN AEYOC AFFNX AGLEN AI. ALMA_UNASSIGNED_HOLDINGS AMVHM AMXXU AQTUD AWYRJ BCCOT BPLKW C06 CS3 DU5 DWIFK EBS EJD H13 HZ~ IVXBP NA5 NUSFT NY~ O9- P2P PQQKQ TAQ TDBHL TFL TFMCV TFW TN5 TOXWX UB9 UPT UU8 V3K V4Q VH1 WH7 ZY4 .4S .7F .DC .QJ 0BK 29J 30N AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR AAYXX ABCCY ABDBF ABFIM ABHAV ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACAGQ ACTCW ACTIO ACUHS ADGTB AEISY AEOZL AFKVX AFRVT AGCQS AGDLA AGMYJ AGROQ AHDZW AHMOU AIJEM AIYEW AJWEG AKBVH AKOOK ALCKM ALQZU AMEWO AQRUH ARCSS AVBZW BLEHA CAG CCCUG CE4 CITATION COF CRFIH DGEBU DKSSO DMQIW EAP EDO EMK EPL EST ESX E~A E~B GTTXZ HF~ H~9 H~P IPNFZ J.P KYCEM LJTGL M4Z MK~ QCRFL RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TEJ TFT TTHFI TUROJ TUS TWF UT5 UU3 ZGOLN ~S~ ADYSH IQODW 1XC |
| ID | FETCH-LOGICAL-c361t-8928b14933d1fe3510ceaef7e6e7885e0b6f14c810dee4bc6007609a33f24d1e3 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1080_00207168808803674&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-7160 |
| IngestDate | Tue Oct 14 06:56:22 EDT 2025 Mon Jul 21 09:15:54 EDT 2025 Sat Nov 29 02:21:22 EST 2025 Tue Nov 18 21:18:10 EST 2025 Mon Oct 20 23:40:18 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3-4 |
| Keywords | Numerical analysis VLSI circuit Least squares method Parallel processing Systolic network Algorithm Factorization Implementation |
| Language | English |
| License | CC BY 4.0 Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c361t-8928b14933d1fe3510ceaef7e6e7885e0b6f14c810dee4bc6007609a33f24d1e3 |
| ORCID | 0000-0003-2361-055X |
| PageCount | 12 |
| ParticipantIDs | crossref_citationtrail_10_1080_00207168808803674 pascalfrancis_primary_7211088 hal_primary_oai_HAL_hal_00857004v1 informaworld_taylorfrancis_310_1080_00207168808803674 crossref_primary_10_1080_00207168808803674 |
| PublicationCentury | 1900 |
| PublicationDate | 1/1/1988 1988-01-00 1988 |
| PublicationDateYYYYMMDD | 1988-01-01 |
| PublicationDate_xml | – month: 01 year: 1988 text: 1/1/1988 day: 01 |
| PublicationDecade | 1980 |
| PublicationPlace | Abingdon |
| PublicationPlace_xml | – name: Abingdon |
| PublicationTitle | International journal of computer mathematics |
| PublicationYear | 1988 |
| Publisher | Gordon and Breach Science Publishers Taylor and Francis Taylor & Francis |
| Publisher_xml | – name: Gordon and Breach Science Publishers – name: Taylor and Francis – name: Taylor & Francis |
| References | Schendel U. (CIT0022) 1984 CIT0021 Leiserson C.E. (CIT0015) 1981 CIT0023 Golub G.H. (CIT0007) 1983 Hwang K. (CIT0011) 1984 Ullman J.D. (CIT0024) 1983 Lawson C. (CIT0014) 1974 Bojanczyk A. (CIT0001) 1981 Kung H.T. (CIT0012) 1982; 15 CIT0003 Sameh A. (CIT0018) 1977 CIT0002 CIT0013 CIT0005 CIT0016 CIT0004 Sameh A. (CIT0020) 1983 CIT0006 CIT0017 CIT0009 CIT0008 Horwarth S. (CIT0010) 1980 CIT0019 |
| References_xml | – ident: CIT0005 doi: 10.1117/12.932507 – ident: CIT0008 doi: 10.1137/1020096 – volume-title: Matrix Computations year: 1983 ident: CIT0007 – volume-title: Solving Least Squares Problems year: 1974 ident: CIT0014 – volume-title: Introduction to Numerical Methods for Parallel Computers year: 1984 ident: CIT0022 – ident: CIT0004 doi: 10.1109/PROC.1966.5273 – ident: CIT0013 – ident: CIT0009 – volume-title: Ph.D Thesis year: 1981 ident: CIT0015 – ident: CIT0003 doi: 10.1145/6490.214102 – volume-title: Numerically stable solution of dense systems of linear equations using mesh-connected processors year: 1981 ident: CIT0001 – ident: CIT0006 doi: 10.1016/0024-3795(80)90156-1 – start-page: 129 year: 1983 ident: CIT0020 publication-title: Bull. EDF – volume-title: Computational Aspects of VLSI year: 1983 ident: CIT0024 – ident: CIT0002 doi: 10.1007/BF01389871 – start-page: 21 volume-title: Proc. Digital Signal Processing year: 1980 ident: CIT0010 – start-page: 207 volume-title: High Speed Computer and Algorithm Organization year: 1977 ident: CIT0018 – ident: CIT0023 – ident: CIT0017 doi: 10.1007/BF01389639 – ident: CIT0021 doi: 10.1145/322047.322054 – ident: CIT0016 doi: 10.1145/322358.322366 – ident: CIT0019 – volume: 15 start-page: 37 year: 1982 ident: CIT0012 publication-title: IEEE Computer doi: 10.1109/MC.1982.1653825 – volume-title: Parallel Processing and Computer Architecture year: 1984 ident: CIT0011 |
| SSID | ssj0008976 |
| Score | 1.3016498 |
| Snippet | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an... |
| SourceID | hal pascalfrancis crossref informaworld |
| SourceType | Open Access Repository Index Database Enrichment Source Publisher |
| StartPage | 287 |
| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences B.7.1 [Integrated circuits] Computer Science Computer science; control theory; systems Distributed, Parallel, and Cluster Computing Exact sciences and technology F.2.1 [Analysis of algorithms and problem complexity] F.l.l [Computation by abstract devices] Givens rotations linear least squares problems Models fo Computation-Systolic array Numerical algorithms and problems-QR decomposition of a dense matrix QR factorization Systolic algorithms Theoretical computing Types and design styles-Algorithms implemented in hardware VLSI VLSI architectures |
| Title | Systolic givens factorization of dense rectangular matrices |
| URI | https://www.tandfonline.com/doi/abs/10.1080/00207168808803674 https://inria.hal.science/hal-00857004 |
| Volume | 25 |
| WOSCitedRecordID | wos10_1080_00207168808803674&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAWR databaseName: Taylor & Francis customDbUrl: eissn: 1029-0265 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008976 issn: 0020-7160 databaseCode: TFW dateStart: 19640101 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA86fPDF-YlTJ0F8EgrN2rUpPg1x7GEMH6burSTtRQXdZK37-71Ls7KJ7EGhFFquScld7iO5_I6xa5X7vvE7ysuzSHshPnlK002hb2FELMEi8D0N49FITibJg8vNKVxaJcXQpgKKsLqaJrfSxTIjjk5wo2GMUPLwCqKY0EDRq6eEvnH_udbDMrGl5YjaQ_J6T_O3Ftas0varzYlcRS6llElV4KiZqtzFig3qN__59_tszzmfvFdJywHbgukhay4LO3A3z4_YLeGYE2AwfyFlWPCqKo87sslnhqO2KoCTtqT1ToyO-YfF-ofimD3278d3A89VWfCyIBKlJ5OO1BgnBUEuDAQ4RzNQYGKIAMPjLvg6MiLMpPBzgFBnkd3MSxSyshPmAoIT1pjOpnDKONpDDEojdDIhCMOu0YT_SC5PDtqgK9Ri_nKU08xBkFMljPdU1EilPwanxW7qTz4r_I1NxFfIupqOkLMHvWFK75ZI_gvRYt1VzqalXRlxfE2DDY2310Sg7sbG0FKe_bHdc7YrEimrZZ0L1ijnX9BmO9mifCvml1akvwGxa_CB |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60CnqxPrFqdRFPQiDbpOkGT0UsFWvxULW3kMesCtpKE_v7ndmkoRXpQSEEEiabsDM7r518A3ARJrat7UZoJbEXWS5dWWHEp5B8Cy1bCg0C31Ov1e-r4dB_KBJuaVFWyTG0zoEijK7mxc3J6FlJHP_CTZbRI9Gjw_Fa7iqscWc6Dr4GnedSEyvfNJdjcovoy13N34ZYsEurr6Yqch67lIsmw5TmTecNL-asUKf63-_fhq3C_xTtXGB2YAVHu1Cd9XYQxVLfgyuGMmfMYPHC-jAVeWOe4q9NMdaCFFaKghUmpzwpQBYfBu4f03147NwMrrtW0WjBih1PZpbyGyqiUMlxEqnRoWUaY4i6hR5ShNxEO_K0dGMl7QTRjWLP7Of5IXGz4SYSnQOojMYjPARBJpHiUo_8THRct6kjhoBkryfBSJM3VAN7Ns1BXKCQczOM90CWYKU_JqcGl-UjnzkExzLic-JdScfg2d12L-B7MzD_qaxBc561QWaSIwVjA2fJ4PUFGShfY8JopY7-OO4ZbHQH972gd9u_O4ZN6SuVZ3lOoJJNvrAO6_E0e0snp0a-vwHjhfSk |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED90ivji_MSp0yA-CYVm7boUn4Y6Jo6xh6l7K_24qKDbWOf-fu_Srmwie1AohZZrUnKX-0guvwO4ChPb1nYttJLYiyyXnqww4ltIvoWWDYUGge-50-h21WDg9_LcnDRPq-QYWmdAEUZX8-QeJ3qeEccnuMkweiR5dDlew12HDXKb6yzU_dZLoYiVb2rLMblF9MWm5m9NLJml9TeTFLkIXco5k2FKw6azehcLRqhV_ufv78JO7n2KZiYue7CGw30ozys7iHyiH8ANA5kzYrB4ZW2YiqwsT35mU4y0IHWVomB1yQueFB6LTwP2j-khPLXu-7dtKy-zYMWOJ6eW8msqokDJcRKp0aFJGmOIuoEeUnxcRzvytHRjJe0E0Y1iz-zm-SHxsuYmEp0jKA1HQzwGQQaRolKPvEx0XLeuIwaAZJ8nwUiTL1QBez7KQZxjkHMpjI9AFlClPwanAtfFJ-MMgGMV8SWxrqBj6Ox2sxPwuzmU_0xWoL7I2WBqlkZyvgbOisarSyJQdGOCaKVO_tjuBWz17lpB56H7eArb0lcqW-I5g9J08oVV2Ixn0_d0cm6k-xsD6PNW |
| 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=Systolic+Givens+factorization+of+dense+rectangular+matrices&rft.jtitle=International+journal+of+computer+mathematics&rft.au=COSNARD%2C+M&rft.au=ROBERT%2C+Y&rft.date=1988&rft.pub=Taylor+and+Francis&rft.issn=0020-7160&rft.volume=25&rft.issue=3-4&rft.spage=287&rft.epage=298&rft_id=info:doi/10.1080%2F00207168808803674&rft.externalDBID=n%2Fa&rft.externalDocID=7211088 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-7160&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-7160&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-7160&client=summon |