{"id":"https://openalex.org/W2610012734","doi":"https://doi.org/10.1137/17m1129830","title":"A Robust and Efficient Implementation of LOBPCG","display_name":"A Robust and Efficient Implementation of LOBPCG","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2610012734","doi":"https://doi.org/10.1137/17m1129830","mag":"2610012734"},"language":"en","primary_location":{"id":"doi:10.1137/17m1129830","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129830","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/1704.07458","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031751484","display_name":"Jed A. Duersch","orcid":"https://orcid.org/0000-0002-2178-3695"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jed A. Duersch","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047489767","display_name":"Meiyue Shao","orcid":"https://orcid.org/0000-0002-4914-7666"},"institutions":[{"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meiyue Shao","raw_affiliation_strings":["Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"],"raw_orcid":"https://orcid.org/0000-0002-4914-7666","affiliations":[{"raw_affiliation_string":"Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005718995","display_name":"Chao Yang","orcid":"https://orcid.org/0000-0001-7426-6248"},"institutions":[{"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chao Yang","raw_affiliation_strings":["Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103226688","display_name":"Ming Gu","orcid":"https://orcid.org/0009-0005-2951-5256"},"institutions":[{"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/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ming Gu","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA 94720","Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5031751484"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":3.2239,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.92746931,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"40","issue":"5","first_page":"C655","last_page":"C676"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9717000126838684,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9337000250816345,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7720395922660828},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7592616677284241},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7003701329231262},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6825234889984131},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5402685403823853},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44783899188041687},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4320945143699646},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4283590316772461},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40770506858825684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21262389421463013}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7720395922660828},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7592616677284241},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7003701329231262},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6825234889984131},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5402685403823853},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44783899188041687},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4320945143699646},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4283590316772461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40770506858825684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21262389421463013},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1129830","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129830","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:1704.07458","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.07458","pdf_url":"https://arxiv.org/pdf/1704.07458","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:ark:/13030/qt7c90z1hr","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:escholarship.org/ark:/13030/qt7c90z1hr","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/7c90z1hr","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol 40, iss 5","raw_type":"article"},{"id":"pmh:oai:osti.gov:1525270","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1525270","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"pmh:qt7c90z1hr","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/7c90z1hr","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Duersch, JA; Shao, M; Yang, C; &amp; Gu, M. (2017). A robust and efficient implementation of LOBPCG. Lawrence Berkeley National Laboratory: Retrieved from: http://www.escholarship.org/uc/item/7c90z1hr","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1704.07458","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.07458","pdf_url":"https://arxiv.org/pdf/1704.07458","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W658559791","https://openalex.org/W1988425770","https://openalex.org/W2001135345","https://openalex.org/W2013737143","https://openalex.org/W2014807599","https://openalex.org/W2040436854","https://openalex.org/W2051142108","https://openalex.org/W2053107666","https://openalex.org/W2086666883","https://openalex.org/W2099611016","https://openalex.org/W2141704677","https://openalex.org/W2160919049","https://openalex.org/W2507702484","https://openalex.org/W2553204845","https://openalex.org/W2557039832","https://openalex.org/W2604250686","https://openalex.org/W2798909945","https://openalex.org/W3022136271","https://openalex.org/W3102398037","https://openalex.org/W3124361461"],"related_works":["https://openalex.org/W2544771389","https://openalex.org/W2034060070","https://openalex.org/W4229957265","https://openalex.org/W2386899346","https://openalex.org/W3082608044","https://openalex.org/W2131505227","https://openalex.org/W2375597358","https://openalex.org/W3087397739","https://openalex.org/W3123621400","https://openalex.org/W1608017769"],"abstract_inverted_index":{"Locally":[0],"Optimal":[1],"Block":[2],"Preconditioned":[3],"Conjugate":[4],"Gradient":[5],"(LOBPCG)":[6],"is":[7,27,33,44,73],"widely":[8],"used":[9],"to":[10,41,76],"compute":[11],"eigenvalues":[12],"of":[13,39,89],"large":[14],"sparse":[15],"symmetric":[16],"matrices.":[17],"The":[18],"algorithm":[19],"can":[20],"suffer":[21],"from":[22],"numerical":[23],"instability":[24],"if":[25],"it":[26],"not":[28],"implemented":[29],"with":[30],"care.":[31],"This":[32],"especially":[34],"problematic":[35],"when":[36],"the":[37,78],"number":[38],"eigenpairs":[40],"be":[42],"computed":[43],"relatively":[45],"large.":[46],"In":[47],"this":[48],"paper":[49],"we":[50],"propose":[51],"an":[52],"improved":[53],"basis":[54],"selection":[55],"strategy":[56],"based":[57],"on":[58],"earlier":[59],"work":[60],"by":[61],"Hetmaniuk":[62],"and":[63,100,109],"Lehoucq":[64],"as":[65,67],"well":[66],"a":[68],"robust":[69],"convergence":[70],"criterion":[71],"which":[72],"backward":[74],"stable":[75],"enhance":[77],"robustness.":[79],"We":[80],"also":[81],"suggest":[82],"several":[83],"algorithmic":[84],"optimizations":[85],"that":[86,96],"improve":[87],"performance":[88],"practical":[90],"LOBPCG":[91],"implementations.":[92],"Numerical":[93],"examples":[94],"confirm":[95],"our":[97],"approach":[98],"consistently":[99],"significantly":[101],"outperforms":[102],"previous":[103],"competing":[104],"approaches":[105],"in":[106],"both":[107],"stability":[108],"speed.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
