{"id":"https://openalex.org/W1415141384","doi":"https://doi.org/10.1137/15m1026080","title":"A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices","display_name":"A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1415141384","doi":"https://doi.org/10.1137/15m1026080","mag":"1415141384"},"language":"en","primary_location":{"id":"doi:10.1137/15m1026080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1026080","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.07157","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038211364","display_name":"Per\u2010Gunnar Martinsson","orcid":"https://orcid.org/0000-0002-1048-5270"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Per-Gunnar Martinsson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020107186","display_name":"Sergey Voronin","orcid":"https://orcid.org/0000-0001-8443-3222"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergey Voronin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1707,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.90131548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"5","first_page":"S485","last_page":"S507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.9943000078201294,"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/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8055213689804077},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.8037400245666504},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6644191145896912},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6253223419189453},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.622327983379364},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6124642491340637},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5844483375549316},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5507513284683228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5421358942985535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5104981660842896},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5090765357017517},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4947745203971863},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.45855778455734253},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.41846275329589844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3363649249076843},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.29832884669303894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14585044980049133},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10322517156600952}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8055213689804077},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.8037400245666504},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6644191145896912},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6253223419189453},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.622327983379364},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6124642491340637},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5844483375549316},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5507513284683228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5421358942985535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5104981660842896},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5090765357017517},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4947745203971863},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.45855778455734253},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.41846275329589844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3363649249076843},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29832884669303894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14585044980049133},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10322517156600952},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":4,"locations":[{"id":"doi:10.1137/15m1026080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1026080","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.07157","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.07157","pdf_url":"https://arxiv.org/pdf/1503.07157","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1415141384","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1503.07157","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1503.07157","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.07157","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.07157","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.07157","pdf_url":"https://arxiv.org/pdf/1503.07157","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1884950711","display_name":null,"funder_award_id":"N66001-13-1-4050","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G5590682888","display_name":"EXTREEMS - QED: Directions in Data Discovery (Data Cubed) in Undergraduate Education","funder_award_id":"1407340","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1415141384.pdf","grobid_xml":"https://content.openalex.org/works/W1415141384.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2004026774","https://openalex.org/W2038922352","https://openalex.org/W2040387238","https://openalex.org/W2052087587","https://openalex.org/W2057261601","https://openalex.org/W2117756735","https://openalex.org/W2119233169","https://openalex.org/W2152356156","https://openalex.org/W2157237396","https://openalex.org/W2952639524"],"related_works":["https://openalex.org/W2159856836","https://openalex.org/W2903666957","https://openalex.org/W2594418358","https://openalex.org/W3048398186","https://openalex.org/W2084348954","https://openalex.org/W3046278820","https://openalex.org/W2624472532","https://openalex.org/W3042443218","https://openalex.org/W2986784331","https://openalex.org/W2560170602","https://openalex.org/W2016579417","https://openalex.org/W2766826645","https://openalex.org/W3083213737","https://openalex.org/W3039986651","https://openalex.org/W2951641596","https://openalex.org/W2911184731","https://openalex.org/W2553204845","https://openalex.org/W2303053974","https://openalex.org/W1613527773","https://openalex.org/W2608773047"],"abstract_inverted_index":{"This":[0],"manuscript":[1],"describes":[2],"a":[3,12,17,27],"technique":[4],"for":[5,140],"computing":[6],"partial":[7,13,18],"rank-revealing":[8],"factorizations,":[9],"such":[10],"as":[11,25,148,150],"QR":[14,152],"factorization":[15,41,67],"or":[16],"singular":[19],"value":[20],"decomposition.":[21],"The":[22,61,88],"method":[23,90,107],"takes":[24],"input":[26],"tolerance":[28],"$\\varepsilon$":[29,50],"and":[30,36,97,122,153],"an":[31,38,70],"$m\\times":[32],"n$":[33],"matrix":[34,142],"$\\boldsymbol{\\mathsf{A}}$":[35,43],"returns":[37],"approximate":[39],"low-rank":[40],"of":[42,64,72,136],"that":[44,133,143],"is":[45,69,75,91,139,154,160],"accurate":[46],"to":[47,83,112,119],"within":[48],"precision":[49],"in":[51,76,164],"the":[52,65,73,84,94,99,106,134,137],"Frobenius":[53],"norm":[54],"(or":[55],"some":[56],"other":[57],"easily":[58],"computed":[59,66],"norm).":[60],"rank":[62],"$k$":[63],"(which":[68],"output":[71],"algorithm)":[74],"all":[77],"examples":[78],"we":[79],"examined":[80],"very":[81],"close":[82],"theoretically":[85],"optimal":[86],"$\\varepsilon$-rank.":[87],"proposed":[89],"inspired":[92],"by":[93,127],"Gram--Schmidt":[95],"algorithm":[96],"has":[98],"same":[100],"$O(mnk)$":[101],"asymptotic":[102],"flop":[103],"count.":[104],"However,":[105],"relies":[108],"on":[109,166],"randomized":[110],"sampling":[111],"avoid":[113],"column":[114],"pivoting,":[115],"which":[116],"allows":[117],"it":[118],"be":[120],"blocked,":[121],"hence":[123],"accelerates":[124],"practical":[125],"computations":[126],"reducing":[128],"communication.":[129],"Numerical":[130],"experiments":[131],"demonstrate":[132],"accuracy":[135],"scheme":[138],"every":[141],"was":[144],"tried":[145],"at":[146],"least":[147],"good":[149],"column-pivoted":[151],"sometimes":[155],"much":[156],"better.":[157],"Computational":[158],"speed":[159],"also":[161],"improved":[162],"substantially,":[163],"particular":[165],"GPU":[167],"architectures.":[168]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}