{"id":"https://openalex.org/W3000463452","doi":"https://doi.org/10.3390/electronics9010182","title":"FPGA-Based Hardware Matrix Inversion Architecture Using Hybrid Piecewise Polynomial Approximation Systolic Cells","display_name":"FPGA-Based Hardware Matrix Inversion Architecture Using Hybrid Piecewise Polynomial Approximation Systolic Cells","publication_year":2020,"publication_date":"2020-01-18","ids":{"openalex":"https://openalex.org/W3000463452","doi":"https://doi.org/10.3390/electronics9010182","mag":"3000463452"},"language":"en","primary_location":{"id":"doi:10.3390/electronics9010182","doi":"https://doi.org/10.3390/electronics9010182","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/electronics9010182","pdf_url":"https://www.mdpi.com/2079-9292/9/1/182/pdf?version=1579326047","source":{"id":"https://openalex.org/S4210202905","display_name":"Electronics","issn_l":"2079-9292","issn":["2079-9292"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-9292/9/1/182/pdf?version=1579326047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045306073","display_name":"Javier V\u00e1zquez Castillo","orcid":"https://orcid.org/0000-0002-0465-8948","observed_orcids":["https://orcid.org/0000-0002-0465-8948"]},"institutions":[{"id":"https://openalex.org/I154691954","display_name":"University of Quintana Roo","ror":"https://ror.org/029w3ge75","country_code":"MX","type":"education","lineage":["https://openalex.org/I154691954"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Javier V\u00e1zquez-Castillo","raw_affiliation_strings":["Department of Engineering, University of Quintana Roo, Chetumal 77019, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-0465-8948","affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Quintana Roo, Chetumal 77019, Mexico","institution_ids":["https://openalex.org/I154691954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000392390","display_name":"Alejandro Castillo-Atoche","orcid":"https://orcid.org/0000-0002-0956-5994","observed_orcids":["https://orcid.org/0000-0002-0956-5994"]},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Alejandro Castillo-Atoche","raw_affiliation_strings":["Department of Mechatronics, Autonomous University of Yucat\u00e1n, M\u00e9rida 97203, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-0956-5994","affiliations":[{"raw_affiliation_string":"Department of Mechatronics, Autonomous University of Yucat\u00e1n, M\u00e9rida 97203, Mexico","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039613458","display_name":"Roberto Carrasco-Alvarez","orcid":"https://orcid.org/0000-0001-9656-8415","observed_orcids":["https://orcid.org/0000-0001-9656-8415"]},"institutions":[{"id":"https://openalex.org/I193181351","display_name":"Universidad de Guadalajara","ror":"https://ror.org/043xj7k26","country_code":"MX","type":"education","lineage":["https://openalex.org/I193181351"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Roberto Carrasco-Alvarez","raw_affiliation_strings":["Department of Electronics, University of Guadalajara, Guadalajara 44430, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, University of Guadalajara, Guadalajara 44430, Mexico","institution_ids":["https://openalex.org/I193181351"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020234193","display_name":"Omar Longoria\u2010Gandara","orcid":"https://orcid.org/0000-0002-9239-0821","observed_orcids":["https://orcid.org/0000-0002-9239-0821"]},"institutions":[{"id":"https://openalex.org/I113686770","display_name":"Instituto Tecnol\u00f3gico y de Estudios Superiores de Occidente","ror":"https://ror.org/00cwp6m07","country_code":"MX","type":"education","lineage":["https://openalex.org/I113686770"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Omar Longoria-Gandara","raw_affiliation_strings":["Department of Electronics, Systems and IT, Western Institute of Technology and Higher Education, Tlaquepaque 45604, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Systems and IT, Western Institute of Technology and Higher Education, Tlaquepaque 45604, Mexico","institution_ids":["https://openalex.org/I113686770"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072302641","display_name":"Jaime Orteg\u00f3n-Aguilar","orcid":"https://orcid.org/0000-0001-8595-1355","observed_orcids":["https://orcid.org/0000-0001-8595-1355"]},"institutions":[{"id":"https://openalex.org/I154691954","display_name":"University of Quintana Roo","ror":"https://ror.org/029w3ge75","country_code":"MX","type":"education","lineage":["https://openalex.org/I154691954"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jaime Orteg\u00f3n-Aguilar","raw_affiliation_strings":["Department of Engineering, University of Quintana Roo, Chetumal 77019, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-8595-1355","affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Quintana Roo, Chetumal 77019, Mexico","institution_ids":["https://openalex.org/I154691954"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5039613458"],"corresponding_institution_ids":["https://openalex.org/I193181351"],"apc_list":{"value":1500,"currency":"CHF","value_usd":1584},"apc_paid":{"value":1500,"currency":"CHF","value_usd":1584},"fwci":1.2137,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.78120636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"9","issue":"1","first_page":"182","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9092000126838684,"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":0.9092000126838684,"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/T13292","display_name":"Embedded Systems and FPGA Applications","score":0.025800000876188278,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.023099999874830246,"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/matrix-inversion","display_name":"matrix inversion","score":0.871999979019165},{"id":"https://openalex.org/keywords/fpga-architecture","display_name":"FPGA architecture","score":0.6480000019073486},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.7400000095367432},{"id":"https://openalex.org/keywords/givens-rotations","display_name":"Givens rotations","score":0.9599999785423279},{"id":"https://openalex.org/keywords/back-substitution","display_name":"back substitution","score":0.6859999895095825},{"id":"https://openalex.org/keywords/piecewise-polynomial-approximation","display_name":"piecewise polynomial approximation","score":0.8930000066757202},{"id":"https://openalex.org/keywords/hybrid-segmentation","display_name":"hybrid segmentation","score":0.9380000233650208},{"id":"https://openalex.org/keywords/hardware-acceleration","display_name":"hardware acceleration","score":0.4090000092983246},{"id":"https://openalex.org/keywords/signal-to-quantization-noise-ratio","display_name":"signal-to-quantization noise ratio","score":0.6259999871253967},{"id":"https://openalex.org/keywords/resource-utilization","display_name":"resource utilization","score":0.5070000290870667}],"concepts":[{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.8176230192184448},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.7040701508522034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6931032538414001},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6129211783409119},{"id":"https://openalex.org/C150741067","wikidata":"https://www.wikidata.org/wiki/Q2377218","display_name":"Systolic array","level":3,"score":0.591204047203064},{"id":"https://openalex.org/C2777674469","wikidata":"https://www.wikidata.org/wiki/Q20741011","display_name":"Virtex","level":3,"score":0.5777366161346436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4574818015098572},{"id":"https://openalex.org/C142962650","wikidata":"https://www.wikidata.org/wiki/Q240838","display_name":"Reconfigurable computing","level":3,"score":0.43660280108451843},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.42834991216659546},{"id":"https://openalex.org/C65232700","wikidata":"https://www.wikidata.org/wiki/Q5656403","display_name":"Hardware architecture","level":3,"score":0.42334628105163574},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.4008329510688782},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.2221599519252777},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.1762220561504364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16567480564117432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/electronics9010182","doi":"https://doi.org/10.3390/electronics9010182","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/electronics9010182","pdf_url":"https://www.mdpi.com/2079-9292/9/1/182/pdf?version=1579326047","source":{"id":"https://openalex.org/S4210202905","display_name":"Electronics","issn_l":"2079-9292","issn":["2079-9292"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e9220762720c4c5fb6d550c72f7ef64a","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/e9220762720c4c5fb6d550c72f7ef64a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronics, Vol 9, Iss 1, p 182 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/electronics9010182","doi":"https://doi.org/10.3390/electronics9010182","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/electronics9010182","pdf_url":"https://www.mdpi.com/2079-9292/9/1/182/pdf?version=1579326047","source":{"id":"https://openalex.org/S4210202905","display_name":"Electronics","issn_l":"2079-9292","issn":["2079-9292"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G486975852","display_name":null,"funder_award_id":"241272","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000463452.pdf","grobid_xml":"https://content.openalex.org/works/W3000463452.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W640910350","https://openalex.org/W1587654378","https://openalex.org/W1969653665","https://openalex.org/W2001747039","https://openalex.org/W2003222013","https://openalex.org/W2005021404","https://openalex.org/W2012366931","https://openalex.org/W2013443139","https://openalex.org/W2020804487","https://openalex.org/W2033532123","https://openalex.org/W2045307229","https://openalex.org/W2145467259","https://openalex.org/W2155596107","https://openalex.org/W2162491972","https://openalex.org/W2162692637","https://openalex.org/W2283402986","https://openalex.org/W2331130748","https://openalex.org/W2538597015","https://openalex.org/W2544156852","https://openalex.org/W2789139117","https://openalex.org/W2798909945","https://openalex.org/W2803752181","https://openalex.org/W2808265777","https://openalex.org/W2891122644","https://openalex.org/W2908551866","https://openalex.org/W2915739092","https://openalex.org/W2921069710","https://openalex.org/W2962776410"],"related_works":["https://openalex.org/W2283402986","https://openalex.org/W2107971525","https://openalex.org/W3163894804","https://openalex.org/W2019974669","https://openalex.org/W4385374993","https://openalex.org/W7018812487","https://openalex.org/W4313897105","https://openalex.org/W4406894817","https://openalex.org/W2053382486","https://openalex.org/W4211221189"],"abstract_inverted_index":{"The":[0],"hardware":[1,29,200],"of":[2,30,37,102,132,194],"the":[3,28,31,35,42,91,100,119,124,129,133,144,157,176,199],"matrix":[4,80,189],"inversion":[5,81],"architecture":[6,82],"using":[7,51,83],"QR":[8],"decomposition":[9],"with":[10,191],"Givens":[11],"Rotations":[12],"(GR)":[13],"and":[14,55,115,123,147,214,218],"a":[15,93,137,153,192,222],"back":[16],"substitution":[17],"(BS)":[18],"block":[19],"is":[20,48,110,121,126,226],"required":[21],"for":[22,99,184],"many":[23],"signal":[24],"processing":[25],"algorithms.":[26],"However,":[27],"GR":[32],"algorithm":[33],"requires":[34,202],"implementation":[36,101],"complex":[38,134],"operations,":[39],"such":[40],"as":[41],"reciprocal":[43],"square":[44],"root":[45],"(RSR),":[46],"which":[47],"typically":[49],"implemented":[50],"LookUp":[52],"Table":[53],"(LUT)":[54],"COordinate":[56],"Rotation":[57],"DIgital":[58],"Computer":[59],"(CORDICs),":[60],"among":[61],"others,":[62],"conveying":[63],"to":[64,169],"either":[65],"high-area":[66],"consumption":[67],"or":[68],"low":[69],"throughput.":[70],"This":[71,107],"paper":[72],"introduces":[73],"an":[74,113,210],"Field-Programmable":[75],"Gate":[76],"Array":[77],"(FPGA)-based":[78],"full":[79],"hybrid":[84,94,108],"piecewise":[85,103],"polynomial":[86,104],"approximation":[87],"systolic":[88,105],"cells.":[89,106],"In":[90,173],"design,":[92],"segmentation":[95],"technique":[96],"was":[97],"incorporated":[98],"approach":[109],"composed":[111],"by":[112],"external":[114],"internal":[116],"segmentation,":[117],"where":[118],"first":[120],"nonuniform":[122],"second":[125,183],"uniform,":[127],"fitting":[128],"curve":[130],"shape":[131],"functions":[135],"achieving":[136,159],"better":[138],"signal-quantization-to":[139],"noise-ratio;":[140],"furthermore,":[141],"it":[142],"improves":[143],"time":[145],"performance":[146],"area":[148],"resources.":[149],"Experimental":[150],"results":[151],"reveal":[152],"well-balanced":[154],"improvement":[155],"in":[156,167,209],"design":[158,178,201],"high":[160],"throughput":[161],"and,":[162],"hence,":[163],"less":[164],"resource":[165],"utilization":[166],"comparison":[168],"state-of-the-art":[170],"FPGA-based":[171],"architectures.":[172],"our":[174],"study,":[175],"proposed":[177],"achieves":[179],"7.51":[180],"Mega-Matrices":[181],"per":[182],"performing":[185],"4":[186,188],"\u00d7":[187],"operations":[190],"latency":[193],"12":[195],"clock":[196],"cycles;":[197],"meanwhile,":[198],"only":[203],"1474":[204,215],"slice":[205,216],"registers,":[206],"1458":[207],"LUTs":[208,220],"FPGA":[211,223],"Virtex-5":[212],"XC5VLX220T,":[213],"registers":[217],"1378":[219],"when":[221],"Virtex-6":[224],"XC6VLX240T":[225],"used.":[227]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-01-23T00:00:00"}