{"id":"https://openalex.org/W2795701329","doi":"https://doi.org/10.1137/18m1179432","title":"Randomized Subspace Iteration: Analysis of Canonical Angles and Unitarily Invariant Norms","display_name":"Randomized Subspace Iteration: Analysis of Canonical Angles and Unitarily Invariant Norms","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2795701329","doi":"https://doi.org/10.1137/18m1179432","mag":"2795701329"},"language":"en","primary_location":{"id":"doi:10.1137/18m1179432","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1179432","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/1804.02614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045561492","display_name":"Arvind K. Saibaba","orcid":"https://orcid.org/0000-0002-8698-6100"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arvind K. Saibaba","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045561492"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00448073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"1","first_page":"23","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9930999875068665,"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":0.9907000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.7910643815994263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7876255512237549},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.7512730360031128},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6851955652236938},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.583574652671814},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5417561531066895},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.505687952041626},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49703410267829895},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.48991745710372925},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4811343252658844},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.48084530234336853},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4684583842754364},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.4578697681427002},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4357326924800873},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.433369904756546},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3676023483276367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3370899558067322},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31293731927871704},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21077284216880798},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16748365759849548},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12030684947967529}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.7910643815994263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7876255512237549},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.7512730360031128},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6851955652236938},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.583574652671814},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5417561531066895},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.505687952041626},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49703410267829895},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.48991745710372925},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4811343252658844},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48084530234336853},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4684583842754364},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.4578697681427002},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4357326924800873},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.433369904756546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3676023483276367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3370899558067322},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31293731927871704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21077284216880798},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16748365759849548},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12030684947967529},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1179432","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1179432","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.02614","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1804.02614","pdf_url":"https://arxiv.org/pdf/1804.02614","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:2795701329","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.02614.pdf","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.1804.02614","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.02614","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.02614","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1804.02614","pdf_url":"https://arxiv.org/pdf/1804.02614","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/G1091762797","display_name":"OP: Collaborative Research: Novel Feature-Based, Randomized Methods for Large-Scale Inversion","funder_award_id":"1720398","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8022582068","display_name":null,"funder_award_id":"DMS-1720398","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8718544020","display_name":null,"funder_award_id":"DMS 1720398","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/F4320328455","display_name":"Ipsen","ror":"https://ror.org/00d801g55"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2795701329.pdf","grobid_xml":"https://content.openalex.org/works/W2795701329.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W131753375","https://openalex.org/W1534121600","https://openalex.org/W1925032196","https://openalex.org/W1998689980","https://openalex.org/W1999352252","https://openalex.org/W2021795584","https://openalex.org/W2059586807","https://openalex.org/W2087399108","https://openalex.org/W2117756735","https://openalex.org/W2136537636","https://openalex.org/W2170078634","https://openalex.org/W2272541835","https://openalex.org/W2610857016","https://openalex.org/W2654090051","https://openalex.org/W2772646190","https://openalex.org/W2782047334","https://openalex.org/W2798909945","https://openalex.org/W2887082150","https://openalex.org/W2962826067","https://openalex.org/W2963346868","https://openalex.org/W2963441460","https://openalex.org/W2963976838","https://openalex.org/W2964332084","https://openalex.org/W2981825520","https://openalex.org/W3030910590","https://openalex.org/W3100283647","https://openalex.org/W3104590783"],"related_works":["https://openalex.org/W2345528374","https://openalex.org/W2164413888","https://openalex.org/W2519690476","https://openalex.org/W2513236363","https://openalex.org/W2607576944","https://openalex.org/W1644425553","https://openalex.org/W2008997396","https://openalex.org/W2950026228","https://openalex.org/W3082392245","https://openalex.org/W2998511779","https://openalex.org/W2154216006","https://openalex.org/W2601222739","https://openalex.org/W3014264020","https://openalex.org/W2111297856","https://openalex.org/W3106324661","https://openalex.org/W3025093284","https://openalex.org/W1977460615","https://openalex.org/W2963684212","https://openalex.org/W2949812197","https://openalex.org/W2950989697"],"abstract_inverted_index":{"This":[0,54],"paper":[1],"analyzes":[2],"the":[3,8,26,30,33,42,51,56,65,72,75,113,119,122],"randomized":[4],"subspace":[5],"iteration":[6],"for":[7,25,41,58,71],"computation":[9],"of":[10,18,74,121],"low-rank":[11,43],"approximations.":[12],"We":[13],"present":[14,69],"three":[15],"different":[16],"kinds":[17],"bounds.":[19,124],"First,":[20],"we":[21,38,68],"derive":[22,39],"both":[23],"bounds":[24,40,57,70,79,102],"canonical":[27],"angles":[28],"between":[29],"exact":[31],"and":[32,60],"approximate":[34],"singular":[35,76],"subspaces.":[36],"Second,":[37],"approximation":[44],"in":[45,64,82],"any":[46,88],"unitarily":[47],"invariant":[48],"norm":[49],"(including":[50],"Schatten-p":[52],"norm).":[53],"generalizes":[55],"spectral":[59],"Frobenius":[61],"norms":[62],"found":[63],"literature.":[66],"Third,":[67],"accuracy":[73],"values.":[77],"The":[78],"are":[80,85,103],"structural":[81],"that":[83,96],"they":[84],"applicable":[86],"to":[87],"starting":[89,114],"guess,":[90],"be":[91],"it":[92],"random":[93,108],"or":[94],"deterministic,":[95],"satisfies":[97],"some":[98],"minimal":[99],"assumptions.":[100],"Specialized":[101],"provided":[104],"when":[105],"a":[106],"Gaussian":[107],"matrix":[109],"is":[110],"used":[111],"as":[112],"guess.":[115],"Numerical":[116],"experiments":[117],"demonstrate":[118],"effectiveness":[120],"proposed":[123]},"counts_by_year":[],"updated_date":"2026-06-07T08:38:57.713557","created_date":"2025-10-10T00:00:00"}
