{"id":"https://openalex.org/W2039917338","doi":"https://doi.org/10.1145/1824801.1824805","title":"Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method","display_name":"Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2039917338","doi":"https://doi.org/10.1145/1824801.1824805","mag":"2039917338"},"language":"en","primary_location":{"id":"doi:10.1145/1824801.1824805","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1824801.1824805","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052397462","display_name":"Ichitaro Yamazaki","orcid":"https://orcid.org/0000-0002-6196-2508"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ichitaro Yamazaki","raw_affiliation_strings":["University of California, Davis","university of california, davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"university of california, davis","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053733794","display_name":"Zhaojun Bai","orcid":"https://orcid.org/0000-0002-1143-2429"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaojun Bai","raw_affiliation_strings":["University of California, Davis","university of california, davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"university of california, davis","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066426676","display_name":"Horst D. Simon","orcid":"https://orcid.org/0000-0003-0832-3720"},"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":"Horst Simon","raw_affiliation_strings":["Lawrence Berkeley National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091144208","display_name":"Lin\u2010Wang Wang","orcid":"https://orcid.org/0000-0001-7061-2692"},"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":"Lin-Wang Wang","raw_affiliation_strings":["Lawrence Berkeley National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043129695","display_name":"Kesheng Wu","orcid":"https://orcid.org/0000-0002-6907-3393"},"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":"Kesheng Wu","raw_affiliation_strings":["Lawrence Berkeley National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5424,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.88938011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"3","first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.8620882630348206},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.8258516788482666},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7138893604278564},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6702896952629089},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.6514152884483337},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6280320882797241},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6203647255897522},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5399093627929688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5331259369850159},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4982016086578369},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48930904269218445},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48926159739494324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42247137427330017},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.4136372208595276},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3394400477409363},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.29444432258605957},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.255806028842926},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10598686337471008},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09601792693138123}],"concepts":[{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.8620882630348206},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.8258516788482666},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7138893604278564},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6702896952629089},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.6514152884483337},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6280320882797241},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6203647255897522},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5399093627929688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5331259369850159},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4982016086578369},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48930904269218445},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48926159739494324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42247137427330017},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.4136372208595276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3394400477409363},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.29444432258605957},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.255806028842926},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10598686337471008},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09601792693138123},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1824801.1824805","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1824801.1824805","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G514736249","display_name":null,"funder_award_id":"DE-FC02-06ER25794","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5528049193","display_name":null,"funder_award_id":"DMS-0611548OCI-0749217","funder_id":"https://openalex.org/F4320337377","funder_display_name":"Office of Advanced Cyberinfrastructure"},{"id":"https://openalex.org/G5935625056","display_name":null,"funder_award_id":"DMS-0611548OCI-0749217","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7368046788","display_name":null,"funder_award_id":"DE-AC02-05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W205839648","https://openalex.org/W1153337856","https://openalex.org/W1506690472","https://openalex.org/W1563653928","https://openalex.org/W1591294031","https://openalex.org/W1760551737","https://openalex.org/W1964217357","https://openalex.org/W1965358692","https://openalex.org/W1971313434","https://openalex.org/W1979655951","https://openalex.org/W1980357388","https://openalex.org/W1981745143","https://openalex.org/W1983055772","https://openalex.org/W2001839700","https://openalex.org/W2035864055","https://openalex.org/W2059586807","https://openalex.org/W2069262775","https://openalex.org/W2077964086","https://openalex.org/W2092022187","https://openalex.org/W2098432400","https://openalex.org/W2116732229","https://openalex.org/W2117686912","https://openalex.org/W2154976136","https://openalex.org/W2160756803","https://openalex.org/W2324350539","https://openalex.org/W4232347666","https://openalex.org/W4285719527","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W1964004266","https://openalex.org/W2048659456","https://openalex.org/W1977732568","https://openalex.org/W4242776319","https://openalex.org/W1964074933","https://openalex.org/W4301683480","https://openalex.org/W2889932903","https://openalex.org/W3166616159","https://openalex.org/W4287126381","https://openalex.org/W1599640686"],"abstract_inverted_index":{"The":[0,15],"Thick-Restart":[1],"Lanczos":[2],"(TRLan)":[3],"method":[4,8,19],"is":[5],"an":[6,38,54,69],"effective":[7],"for":[9],"solving":[10],"large-scale":[11],"Hermitian":[12],"eigenvalue":[13],"problems.":[14],"performance":[16],"of":[17,25,45,48,91],"the":[18,23,26,43,46,60,64,81,88],"strongly":[20],"depends":[21],"on":[22],"dimension":[24,61],"projection":[27],"subspace":[28,49],"used":[29],"at":[30],"each":[31],"restart.":[32],"In":[33],"this":[34,77],"article,":[35],"we":[36],"propose":[37],"objective":[39],"function":[40],"to":[41,57,62,75,86,98],"quantify":[42],"effectiveness":[44],"selection":[47],"dimension,":[50],"and":[51],"then":[52],"introduce":[53],"adaptive":[55,78],"scheme":[56,79],"dynamically":[58],"select":[59],"optimize":[63],"performance.":[65],"We":[66],"have":[67],"developed":[68],"open-source":[70],"software":[71],"package":[72],"a":[73,94,102],"--TRLan":[74,95],"include":[76],"in":[80],"TRLan":[82],"method.":[83],"When":[84],"applied":[85],"calculate":[87],"electronic":[89],"structure":[90],"quantum":[92],"dots,":[93],"runs":[96],"up":[97],"2.3x":[99],"faster":[100],"than":[101],"state-of-the-art":[103],"preconditioned":[104],"conjugate":[105],"gradient":[106],"eigensolver.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-10-10T00:00:00"}
