{"id":"https://openalex.org/W3212944728","doi":"https://doi.org/10.1137/21m1422513","title":"Approximating Matrix Eigenvalues by Subspace Iteration with Repeated Random Sparsification","display_name":"Approximating Matrix Eigenvalues by Subspace Iteration with Repeated Random Sparsification","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W3212944728","doi":"https://doi.org/10.1137/21m1422513","mag":"3212944728"},"language":"en","primary_location":{"id":"doi:10.1137/21m1422513","doi":"https://doi.org/10.1137/21m1422513","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1422513","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/21m1422513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032184863","display_name":"Samuel M. Greene","orcid":"https://orcid.org/0000-0001-5135-5926","observed_orcids":["https://orcid.org/0000-0001-5135-5926"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel M. Greene","raw_affiliation_strings":["Department of Chemistry, Columbia University, New York, New York 10027, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Columbia University, New York, New York 10027, United States","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020598676","display_name":"Robert J. Webber","orcid":"https://orcid.org/0000-0001-8286-6315","observed_orcids":["https://orcid.org/0000-0001-8286-6315"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert J. Webber","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017031564","display_name":"Timothy C. Berkelbach","orcid":"https://orcid.org/0000-0002-7445-2136","observed_orcids":["https://orcid.org/0000-0002-7445-2136"]},"institutions":[{"id":"https://openalex.org/I4387153999","display_name":"Flatiron Institute","ror":"https://ror.org/00sekdz59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338","https://openalex.org/I4387153999"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy C. Berkelbach","raw_affiliation_strings":["Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States","Department of Chemistry, Columbia University, New York, New York 10027, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States","institution_ids":["https://openalex.org/I4387153999"]},{"raw_affiliation_string":"Department of Chemistry, Columbia University, New York, New York 10027, United States","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016587955","display_name":"Jonathan Weare","orcid":"https://orcid.org/0000-0001-8745-1821","observed_orcids":["https://orcid.org/0000-0001-8745-1821"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Weare","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5404,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59737182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"44","issue":"5","first_page":"A3067","last_page":"A3097"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9937000274658203,"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":0.9937000274658203,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/subspace-iteration","display_name":"subspace iteration","score":0.9900000095367432},{"id":"https://openalex.org/keywords/high-dimensional-problems","display_name":"high-dimensional problems","score":0.5609999895095825},{"id":"https://openalex.org/keywords/quantum-chemistry","display_name":"quantum chemistry","score":0.722000002861023},{"id":"https://openalex.org/keywords/iterative-methods","display_name":"iterative methods","score":0.3100000023841858}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7907663583755493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7498507499694824},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6352856159210205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5991393327713013},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.587393581867218},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.5514684915542603},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5181328058242798},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.4870898723602295},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.474331796169281},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4592764973640442},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4213739335536957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.352483868598938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32993417978286743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20867064595222473},{"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},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1422513","doi":"https://doi.org/10.1137/21m1422513","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1422513","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:2103.12109","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.12109","pdf_url":"https://arxiv.org/pdf/2103.12109","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2103.12109","doi":"https://doi.org/10.48550/arxiv.2103.12109","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.12109","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1137/21m1422513","doi":"https://doi.org/10.1137/21m1422513","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1422513","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1695379323","display_name":"ENSEMBLE SIMULATION TECHNIQUES AND FAST RANDOMIZED ALGORITHMS","funder_award_id":"DESC0020427","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G2526998692","display_name":null,"funder_award_id":"DE-SC0020427","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G2958156528","display_name":"RTG: Research Training Group in Mathematical Modeling and Simulation","funder_award_id":"1646339","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4863676306","display_name":"S2I2: Impl: The Molecular Sciences Software Institute","funder_award_id":"1547580","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6726860487","display_name":null,"funder_award_id":"DMS-1646339","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8893973625","display_name":null,"funder_award_id":"OAC-1547580","funder_id":"https://openalex.org/F4320337377","funder_display_name":"Office of Advanced Cyberinfrastructure"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309626","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28"},{"id":"https://openalex.org/F4320319356","display_name":"Flatiron Health","ror":"https://ror.org/0508h6p74"},{"id":"https://openalex.org/F4320319918","display_name":"York University","ror":"https://ror.org/05fq50484"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337377","display_name":"Office of Advanced Cyberinfrastructure","ror":"https://ror.org/04nh1dc89"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W1483514891","https://openalex.org/W1505090736","https://openalex.org/W1524525881","https://openalex.org/W1563653928","https://openalex.org/W1579788182","https://openalex.org/W1584623820","https://openalex.org/W1591018827","https://openalex.org/W1592958377","https://openalex.org/W1683798242","https://openalex.org/W1925032196","https://openalex.org/W1971307635","https://openalex.org/W1972867157","https://openalex.org/W1980362252","https://openalex.org/W1982291654","https://openalex.org/W1995606398","https://openalex.org/W1995713768","https://openalex.org/W1998071870","https://openalex.org/W2009596258","https://openalex.org/W2028302592","https://openalex.org/W2033459956","https://openalex.org/W2033612074","https://openalex.org/W2037363603","https://openalex.org/W2040387238","https://openalex.org/W2051843596","https://openalex.org/W2055939670","https://openalex.org/W2059586807","https://openalex.org/W2062465394","https://openalex.org/W2062736875","https://openalex.org/W2063397409","https://openalex.org/W2080330289","https://openalex.org/W2086160340","https://openalex.org/W2089468765","https://openalex.org/W2089842282","https://openalex.org/W2106606323","https://openalex.org/W2117686912","https://openalex.org/W2117756735","https://openalex.org/W2128728535","https://openalex.org/W2129894766","https://openalex.org/W2133386459","https://openalex.org/W2152452984","https://openalex.org/W2177697562","https://openalex.org/W2202459101","https://openalex.org/W2222698712","https://openalex.org/W2502916351","https://openalex.org/W2520697526","https://openalex.org/W2756519801","https://openalex.org/W2767580618","https://openalex.org/W2769966763","https://openalex.org/W2805191290","https://openalex.org/W2885549115","https://openalex.org/W2909179183","https://openalex.org/W2913059114","https://openalex.org/W2918886142","https://openalex.org/W2944343889","https://openalex.org/W2950669909","https://openalex.org/W2966219945","https://openalex.org/W2998021410","https://openalex.org/W3004525958","https://openalex.org/W3021406965","https://openalex.org/W3021945244","https://openalex.org/W3087024315","https://openalex.org/W3093036756","https://openalex.org/W3098761958","https://openalex.org/W3099212732","https://openalex.org/W3099674394","https://openalex.org/W3104538735","https://openalex.org/W4240959780","https://openalex.org/W4242722506","https://openalex.org/W4292070112"],"related_works":["https://openalex.org/W3137183013","https://openalex.org/W7221789374","https://openalex.org/W3199582388","https://openalex.org/W7100461767","https://openalex.org/W1601452860","https://openalex.org/W1984772310","https://openalex.org/W2063375366","https://openalex.org/W2613712506","https://openalex.org/W2045013565","https://openalex.org/W2119175729"],"abstract_inverted_index":{"Traditional":[0],"numerical":[1],"methods":[2,16,44],"for":[3,10,18,45,55],"calculating":[4],"matrix":[5],"eigenvalues":[6,50],"are":[7],"prohibitively":[8],"expensive":[9],"high-dimensional":[11],"problems.":[12],"Iterative":[13],"random":[14,32],"sparsification":[15],"allow":[17],"the":[19,46],"estimation":[20,47],"of":[21,48],"a":[22,38],"single":[23],"dominant":[24],"eigenvalue":[25],"at":[26],"reduced":[27],"cost":[28],"by":[29],"leveraging":[30],"repeated":[31],"sampling":[33],"and":[34,51],"averaging.":[35],"We":[36],"present":[37],"general":[39],"approach":[40],"to":[41],"extending":[42],"such":[43],"multiple":[49],"demonstrate":[52],"its":[53],"performance":[54],"several":[56],"benchmark":[57],"problems":[58],"in":[59],"quantum":[60],"chemistry.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2021-11-22T00:00:00"}
