{"id":"https://openalex.org/W2077428505","doi":"https://doi.org/10.1145/1661438.1661439","title":"A High Throughput FPGA-Based Floating Point Conjugate Gradient Implementation for Dense Matrices","display_name":"A High Throughput FPGA-Based Floating Point Conjugate Gradient Implementation for Dense Matrices","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2077428505","doi":"https://doi.org/10.1145/1661438.1661439","mag":"2077428505"},"language":"en","primary_location":{"id":"doi:10.1145/1661438.1661439","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1661438.1661439","pdf_url":null,"source":{"id":"https://openalex.org/S112809824","display_name":"ACM Transactions on Reconfigurable Technology and Systems","issn_l":"1936-7406","issn":["1936-7406","1936-7414"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Reconfigurable Technology and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066601894","display_name":"Ant\u00f3nio Rold\u00e3o","orcid":"https://orcid.org/0000-0003-0414-4899"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Antonio Roldao","raw_affiliation_strings":["Imperial College London","Imperial College London,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Imperial College London,#TAB#","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029829952","display_name":"George A. Constantinides","orcid":"https://orcid.org/0000-0002-0201-310X"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"George A. Constantinides","raw_affiliation_strings":["Imperial College London","Imperial College London,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Imperial College London,#TAB#","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066601894"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":5.835,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.96413768,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flops","display_name":"FLOPS","score":0.8426694869995117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8382472991943359},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.7413100004196167},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.7256558537483215},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.7217044830322266},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6510151624679565},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6254597902297974},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5237281918525696},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4856032729148865},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.48008090257644653},{"id":"https://openalex.org/keywords/symmetric-multiprocessor-system","display_name":"Symmetric multiprocessor system","score":0.43208047747612},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.42564696073532104},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4046659767627716},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2398991584777832},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.19726303219795227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.07680919766426086}],"concepts":[{"id":"https://openalex.org/C3826847","wikidata":"https://www.wikidata.org/wiki/Q188768","display_name":"FLOPS","level":2,"score":0.8426694869995117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8382472991943359},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.7413100004196167},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.7256558537483215},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.7217044830322266},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6510151624679565},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6254597902297974},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5237281918525696},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4856032729148865},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.48008090257644653},{"id":"https://openalex.org/C172430144","wikidata":"https://www.wikidata.org/wiki/Q17111997","display_name":"Symmetric multiprocessor system","level":2,"score":0.43208047747612},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.42564696073532104},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4046659767627716},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2398991584777832},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.19726303219795227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.07680919766426086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1661438.1661439","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1661438.1661439","pdf_url":null,"source":{"id":"https://openalex.org/S112809824","display_name":"ACM Transactions on Reconfigurable Technology and Systems","issn_l":"1936-7406","issn":["1936-7406","1936-7414"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Reconfigurable Technology and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.4000000059604645,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G4452853771","display_name":null,"funder_award_id":"EP/G00210X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6672801631","display_name":null,"funder_award_id":"EP/E00024X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6787767956","display_name":null,"funder_award_id":"EP/G031576/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G803588348","display_name":null,"funder_award_id":"EP/C549481/1EP/E00024X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W184056909","https://openalex.org/W612485192","https://openalex.org/W1528618170","https://openalex.org/W1557486844","https://openalex.org/W1581309603","https://openalex.org/W1587258699","https://openalex.org/W1946431381","https://openalex.org/W1983486886","https://openalex.org/W1989154272","https://openalex.org/W2061624656","https://openalex.org/W2064328715","https://openalex.org/W2073061372","https://openalex.org/W2098841537","https://openalex.org/W2099524603","https://openalex.org/W2103817093","https://openalex.org/W2106942255","https://openalex.org/W2115002670","https://openalex.org/W2123017533","https://openalex.org/W2124661136","https://openalex.org/W2131247856","https://openalex.org/W2132158408","https://openalex.org/W2135653967","https://openalex.org/W2136897996","https://openalex.org/W2139774022","https://openalex.org/W2145018926","https://openalex.org/W2145281085","https://openalex.org/W2152567198","https://openalex.org/W2154762785","https://openalex.org/W2163198250","https://openalex.org/W2253792952","https://openalex.org/W2316564661","https://openalex.org/W2798909945","https://openalex.org/W4238913942","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W2146343568","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2560894929","https://openalex.org/W1861262881","https://openalex.org/W2156524298","https://openalex.org/W4385856009","https://openalex.org/W2783386063"],"abstract_inverted_index":{"Recent":[0],"developments":[1],"in":[2,34,50,171],"the":[3,21,38,63,131,193],"capacity":[4],"of":[5,23,29,40,42,98,195,209,220,244,249],"modern":[6,84],"Field":[7],"Programmable":[8],"Gate":[9],"Arrays":[10],"(FPGAs)":[11],"have":[12],"significantly":[13],"expanded":[14],"their":[15],"applications.":[16],"One":[17],"such":[18,60],"field":[19],"is":[20,32,37,62,89,121,127,164],"acceleration":[22],"scientific":[24,35],"computation":[25,36,132],"and":[26,56,76,101,173,177,186,212],"one":[27],"type":[28],"calculation":[30],"that":[31,47,123,236],"commonplace":[33],"solution":[39],"systems":[41,97],"linear":[43,99],"equations.":[44],"A":[45,223],"method":[46],"has":[48],"proven":[49],"software":[51,228],"to":[52,113,129,152,167,183,188],"be":[53,103,184],"very":[54],"efficient":[55],"robust":[57],"for":[58,92,136],"finding":[59],"solutions":[61],"Conjugate":[64],"Gradient":[65],"(CG)":[66],"algorithm.":[67],"In":[68,117],"this":[69,118,237],"article":[70,119],"we":[71],"present":[72],"a":[73,106,150,158,189,202,215,232,241],"widely":[74],"parallel":[75,172],"deeply":[77],"pipelined":[78],"hardware":[79],"CG":[80],"implementation,":[81],"targeted":[82],"at":[83,245],"FPGA":[85,238],"architectures.":[86],"This":[87],"implementation":[88,229,239],"particularly":[90],"suited":[91],"accelerating":[93],"multiple":[94],"small-to-medium-sized":[95],"dense":[96],"equations":[100],"can":[102],"used":[104],"as":[105,110],"stand-alone":[107],"solver":[108],"or":[109],"building":[111],"block":[112],"solve":[114,168],"higher-order":[115],"systems.":[116],"it":[120,126,163],"shown":[122,182],"through":[124],"parallelization":[125],"possible":[128,166],"convert":[130],"time":[133],"per":[134],"iteration":[135],"an":[137,226,247],"order":[138,248],"n":[139,144,155],"matrix":[140,196],"from":[141],"\u0398":[142,153],"(":[143,154],"2":[145],")":[146,156],"clock":[147],"cycles":[148],"on":[149,157,201,214,231],"microprocessor":[151],"FPGA.":[159],"Through":[160],"deep":[161],"pipelining":[162],"also":[165],"several":[169],"problems":[170],"maximize":[174],"both":[175],"performance":[176,208,219],"efficiency.":[178],"I/O":[179],"requirements":[180],"are":[181],"scalable":[185],"convergent":[187],"constant":[190],"value":[191],"with":[192,225],"increase":[194],"order.":[197],"Post":[198],"place-and-route":[199],"results":[200,213],"readily":[203],"available":[204],"VirtexII-6000":[205],"demonstrate":[206,235],"sustained":[207,218],"5":[210],"GFlops,":[211],"Virtex5-330":[216],"indicate":[217],"35":[221],"GFlops.":[222],"comparison":[224],"optimized":[227],"running":[230],"high-end":[233],"CPU":[234],"represents":[240],"significant":[242],"speedup":[243],"least":[246],"magnitude.":[250]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
