{"id":"https://openalex.org/W2087314423","doi":"https://doi.org/10.1137/0911057","title":"QR Factorization of a Dense Matrix on a Hypercube Multiprocessor","display_name":"QR Factorization of a Dense Matrix on a Hypercube Multiprocessor","publication_year":1990,"publication_date":"1990-09-01","ids":{"openalex":"https://openalex.org/W2087314423","doi":"https://doi.org/10.1137/0911057","mag":"2087314423"},"language":"en","primary_location":{"id":"doi:10.1137/0911057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911057","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific and Statistical Computing","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/A5057896006","display_name":"Eleanor Chu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eleanor Chu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082898376","display_name":"Alan D. George","orcid":"https://orcid.org/0000-0001-9665-2879"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan George","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9242,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94806071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"5","first_page":"990","last_page":"1028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9995999932289124,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.9165766835212708},{"id":"https://openalex.org/keywords/multiprocessing","display_name":"Multiprocessing","score":0.8056527972221375},{"id":"https://openalex.org/keywords/intel-ipsc","display_name":"Intel iPSC","score":0.7305307388305664},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.7235187888145447},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.6599553823471069},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5914096236228943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.585686981678009},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5276328921318054},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5187073349952698},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4945089519023895},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.49064913392066956},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.42488545179367065},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4174236059188843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3637428879737854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3242782652378082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14977893233299255},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08222880959510803}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.9165766835212708},{"id":"https://openalex.org/C4822641","wikidata":"https://www.wikidata.org/wiki/Q846651","display_name":"Multiprocessing","level":2,"score":0.8056527972221375},{"id":"https://openalex.org/C199115840","wikidata":"https://www.wikidata.org/wiki/Q108649754","display_name":"Intel iPSC","level":3,"score":0.7305307388305664},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.7235187888145447},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.6599553823471069},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5914096236228943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.585686981678009},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5276328921318054},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5187073349952698},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4945089519023895},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.49064913392066956},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.42488545179367065},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4174236059188843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3637428879737854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3242782652378082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14977893233299255},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08222880959510803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0911057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911057","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific and Statistical Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1599533721","https://openalex.org/W1685044542","https://openalex.org/W1968162948","https://openalex.org/W1974962009","https://openalex.org/W2028704100","https://openalex.org/W2042025615","https://openalex.org/W2054781107","https://openalex.org/W2070376477","https://openalex.org/W2070698221","https://openalex.org/W2084727637","https://openalex.org/W2086564156","https://openalex.org/W2086694627","https://openalex.org/W2089309544","https://openalex.org/W2089863429","https://openalex.org/W2169947360"],"related_works":["https://openalex.org/W3093207677","https://openalex.org/W4250003423","https://openalex.org/W2162737912","https://openalex.org/W2753964365","https://openalex.org/W2221439609","https://openalex.org/W2026686860","https://openalex.org/W2028685923","https://openalex.org/W3046001238","https://openalex.org/W2963531223","https://openalex.org/W1997332808"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"a":[3,12,16,27,56],"new":[4],"algorithm":[5],"for":[6,55],"computing":[7],"the":[8,31,49,61,74,77,84,88,96,99,102,118],"QR":[9],"factorization":[10],"of":[11,59,76,87,95,98,105],"rectangular":[13],"matrix":[14,100],"on":[15,112],"hypercube":[17,22],"multiprocessor":[18,116],"is":[19,24,46,52,65],"described.":[20],"The":[21],"network":[23],"configured":[25,89],"as":[26],"two-dimensional":[28],"subcube-grid":[29],"in":[30,93],"proposed":[32],"scheme.":[33],"A":[34,79],"global":[35],"communication":[36,106],"scheme":[37],"that":[38,54],"uses":[39],"redundant":[40],"computation":[41],"to":[42],"maintain":[43],"data":[44],"proximity":[45],"employed,":[47],"and":[48,67,101,107],"mapping":[50],"strategy":[51],"such":[53],"fixed":[57],"number":[58],"processors":[60],"processor":[62],"idle":[63],"time":[64],"small":[66],"either":[68],"constant":[69],"or":[70],"grows":[71],"linearly":[72],"with":[73],"dimension":[75],"matrix.":[78],"complexity":[80],"analysis":[81],"shows":[82],"what":[83],"aspect":[85],"ratio":[86],"grid":[90],"should":[91],"be":[92],"terms":[94],"shape":[97],"relative":[103],"speeds":[104],"computation.":[108],"Numerical":[109],"experiments":[110],"performed":[111],"an":[113],"Intel":[114],"Hypercube":[115],"support":[117],"theoretical":[119],"results.":[120]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}