{"id":"https://openalex.org/W3215822382","doi":"https://doi.org/10.1137/22m1518396","title":"Randomized Block Gram\u2013Schmidt Process for the Solution of Linear Systems and Eigenvalue Problems","display_name":"Randomized Block Gram\u2013Schmidt Process for the Solution of Linear Systems and Eigenvalue Problems","publication_year":2025,"publication_date":"2025-02-19","ids":{"openalex":"https://openalex.org/W3215822382","doi":"https://doi.org/10.1137/22m1518396","mag":"3215822382"},"language":"en","primary_location":{"id":"doi:10.1137/22m1518396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1518396","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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2111.14641","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042488420","display_name":"Oleg Balabanov","orcid":"https://orcid.org/0009-0004-4069-1448"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Oleg Balabanov","raw_affiliation_strings":["Work performed at Alpines, Inria, Sorbonne Universit\u00e9, Universit\u00e9 de Paris, CNRS, Laboratoire Jacques-Louis Lions, F-75012 Paris, France.\u00a0Current affiliation:\u00a0Department of Statistics, University of California, Berkeley, International Computer Science Institute, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Work performed at Alpines, Inria, Sorbonne Universit\u00e9, Universit\u00e9 de Paris, CNRS, Laboratoire Jacques-Louis Lions, F-75012 Paris, France.\u00a0Current affiliation:\u00a0Department of Statistics, University of California, Berkeley, International Computer Science Institute, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I148283060","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040521001","display_name":"Laura Grigori","orcid":"https://orcid.org/0000-0002-5880-1076"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","FR"],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["Work performed at Alpines, Inria, Sorbonne Universit\u00e9, Universit\u00e9 de Paris, CNRS, Laboratoire Jacques-Louis Lions, F-75012 Paris, France.\u00a0Current affiliation:\u00a0Institute of Mathematics, EPFL and Scientific Computing Division, Paul Scherrer Institute, 5232 Villigen, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Work performed at Alpines, Inria, Sorbonne Universit\u00e9, Universit\u00e9 de Paris, CNRS, Laboratoire Jacques-Louis Lions, F-75012 Paris, France.\u00a0Current affiliation:\u00a0Institute of Mathematics, EPFL and Scientific Computing Division, Paul Scherrer Institute, 5232 Villigen, Switzerland","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1482,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.90616126,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"47","issue":"1","first_page":"A553","last_page":"A585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9986000061035156,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.8027150630950928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6418219208717346},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5611356496810913},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5396061539649963},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.4974203407764435},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.47353121638298035},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4728669822216034},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44340670108795166},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.44176051020622253},{"id":"https://openalex.org/keywords/gramian-matrix","display_name":"Gramian matrix","score":0.41160160303115845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3640892505645752},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33950334787368774},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.17542532086372375}],"concepts":[{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.8027150630950928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6418219208717346},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5611356496810913},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5396061539649963},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.4974203407764435},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.47353121638298035},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4728669822216034},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44340670108795166},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44176051020622253},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.41160160303115845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3640892505645752},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33950334787368774},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.17542532086372375},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/22m1518396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1518396","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:dora:psi_86429","is_oa":false,"landing_page_url":"https://www.dora.lib4ri.ch/psi/item/psi:86429","pdf_url":null,"source":{"id":"https://openalex.org/S4306402574","display_name":"DORA PSI (Paul Scherrer Institute)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802229908","host_organization_name":"Paul Scherrer Institute","host_organization_lineage":["https://openalex.org/I2802229908"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:2111.14641","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.14641","pdf_url":"https://arxiv.org/pdf/2111.14641","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":"pmh:oai:HAL:hal-03469555v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03469555","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2021","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2111.14641","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.14641","pdf_url":"https://arxiv.org/pdf/2111.14641","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/G6617287496","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G7683707404","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3215822382.pdf","grobid_xml":"https://content.openalex.org/works/W3215822382.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W9532344","https://openalex.org/W1907157228","https://openalex.org/W2020804487","https://openalex.org/W2021870845","https://openalex.org/W2064122889","https://openalex.org/W2066349733","https://openalex.org/W2073955633","https://openalex.org/W2107599050","https://openalex.org/W2124659530","https://openalex.org/W2157237396","https://openalex.org/W2157988812","https://openalex.org/W2480854438","https://openalex.org/W2787248994","https://openalex.org/W2792702316","https://openalex.org/W2963455674","https://openalex.org/W2982293719","https://openalex.org/W3023393331","https://openalex.org/W3094385323","https://openalex.org/W3094536092","https://openalex.org/W3099348172","https://openalex.org/W3104590783","https://openalex.org/W3108353645","https://openalex.org/W3112410551","https://openalex.org/W3144545573","https://openalex.org/W3198813152","https://openalex.org/W3205988062","https://openalex.org/W3210555365","https://openalex.org/W4200578327","https://openalex.org/W4250954493","https://openalex.org/W4313421141","https://openalex.org/W4317951399","https://openalex.org/W4399855006"],"related_works":["https://openalex.org/W2002097440","https://openalex.org/W2000690703","https://openalex.org/W3152060313","https://openalex.org/W2484832770","https://openalex.org/W2028770117","https://openalex.org/W2103271089","https://openalex.org/W2127147063","https://openalex.org/W1995841910","https://openalex.org/W1990351032","https://openalex.org/W1596285621"],"abstract_inverted_index":{"This":[0],"article":[1],"introduces":[2],"randomized":[3,15,133],"block":[4,88,97],"Gram-Schmidt":[5,16,40,89],"process":[6],"(RBGS)":[7],"for":[8,100,118],"QR":[9],"decomposition.":[10],"RBGS":[11,68],"extends":[12],"the":[13,87,92,96,101,119],"single-vector":[14],"(RGS)":[17],"algorithm":[18],"and":[19,29,55,115,124,141],"inherits":[20],"its":[21],"key":[22,93],"characteristics":[23],"such":[24],"as":[25,33,36,47],"being":[26],"more":[27],"efficient":[28],"having":[30],"at":[31],"least":[32],"much":[34],"stability":[35],"any":[37],"deterministic":[38],"(block)":[39],"algorithm.":[41],"Block":[42],"algorithms":[43],"offer":[44],"superior":[45],"performance":[46],"they":[48],"are":[49],"based":[50,138],"on":[51,139,144],"BLAS3":[52],"matrix-wise":[53],"operations":[54],"reduce":[56],"communication":[57],"cost":[58],"when":[59],"executed":[60],"in":[61,72,95,108,112],"parallel.":[62],"Notably,":[63],"our":[64],"low-synchronization":[65],"variant":[66],"of":[67,103,121,135],"can":[69],"be":[70],"implemented":[71],"a":[73,104],"parallel":[74],"environment":[75],"using":[76],"only":[77],"one":[78],"global":[79],"reduction":[80],"operation":[81],"between":[82],"processors":[83],"per":[84],"block.":[85],"Moreover,":[86],"orthogonalization":[90],"is":[91,110],"element":[94],"Arnoldi":[98],"procedure":[99],"construction":[102],"Krylov":[105],"basis,":[106],"which":[107],"turn":[109],"used":[111],"GMRES,":[113],"FOM":[114],"Rayleigh-Ritz":[116],"methods":[117],"solution":[120],"linear":[122],"systems":[123],"clustered":[125],"eigenvalue":[126],"problems.":[127],"In":[128],"this":[129],"article,":[130],"we":[131],"develop":[132],"versions":[134],"these":[136],"methods,":[137],"RBGS,":[140],"validate":[142],"them":[143],"nontrivial":[145],"numerical":[146],"examples.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
