{"id":"https://openalex.org/W1586068380","doi":"https://doi.org/10.1137/040613767","title":"An Algebraic Substructuring Method for Large-Scale Eigenvalue Calculation","display_name":"An Algebraic Substructuring Method for Large-Scale Eigenvalue Calculation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1586068380","doi":"https://doi.org/10.1137/040613767","mag":"1586068380"},"language":"en","primary_location":{"id":"doi:10.1137/040613767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613767","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/m2/1/high_res_d/918549.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077547409","display_name":"Chao Yang","orcid":"https://orcid.org/0000-0001-7172-7539"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chao Yang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070142100","display_name":"W.B. Gao","orcid":"https://orcid.org/0009-0003-1647-5596"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weiguo Gao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055283405","display_name":"Zheng\u2010Jian Bai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaojun Bai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048475667","display_name":"X. Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoye S. Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026070952","display_name":"L. Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lie-Quan Lee","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033402901","display_name":"Parry Husbands","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parry Husbands","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056131016","display_name":"Esmond Ng","orcid":"https://orcid.org/0000-0002-4535-6348"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Esmond Ng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5077547409"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6758,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68987678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"3","first_page":"873","last_page":"892"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9943000078201294,"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":0.9943000078201294,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9377999901771545,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7055282592773438},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5376561284065247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5344855785369873},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.524362325668335},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5121933817863464},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4817097783088684},{"id":"https://openalex.org/keywords/structuring","display_name":"Structuring","score":0.4517322778701782},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4304127097129822},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42702335119247437},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4177165627479553},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4140413701534271},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4131457805633545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3427835702896118},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1428898572921753},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13706141710281372}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7055282592773438},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5376561284065247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5344855785369873},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.524362325668335},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5121933817863464},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4817097783088684},{"id":"https://openalex.org/C2775945657","wikidata":"https://www.wikidata.org/wiki/Q381442","display_name":"Structuring","level":2,"score":0.4517322778701782},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4304127097129822},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42702335119247437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4177165627479553},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4140413701534271},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4131457805633545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3427835702896118},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1428898572921753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13706141710281372},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/040613767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613767","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:info:ark/67531/metadc877515","is_oa":true,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/","pdf_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/m2/1/high_res_d/918549.pdf","source":{"id":"https://openalex.org/S4306400792","display_name":"University of North Texas Digital Library (University of North Texas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123534392","host_organization_name":"University of North Texas","host_organization_lineage":["https://openalex.org/I123534392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal Name: Society for Industrial and Applied Mathematics: Journal onMatrix Analysis and Applications; Journal Volume: 27; Journal Issue: 3; Related Information: Journal Publication Date: 2005","raw_type":"Article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt8fw31896","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/8fw31896","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":"","raw_type":"article"},{"id":"pmh:oai:osti.gov:918549","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/918549","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:qt8fw31896","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/8fw31896","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":"Yang, C.; Gao, W.; Bai, Z.; Li, X.; Lee, L.; Husbands, P.; \u00c2\u00a0et al.(2004). An algebraic sub-structuring method for large-scale eigenvalue calculation. Lawrence Berkeley National Laboratory. Lawrence Berkeley National Laboratory: Lawrence Berkeley National Laboratory. Retrieved from: http://www.escholarship.org/uc/item/8fw31896","raw_type":"article"},{"id":"mag:2281669617","is_oa":false,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/m2/1/high_res_d/918549.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null},{"id":"mag:1586068380","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/8fw31896.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764971142","display_name":"Lawrence Berkeley National Laboratory","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800592","host_organization_name":"United States Department of Energy","host_organization_lineage":["https://openalex.org/P4320800592"],"host_organization_lineage_names":["United States Department of Energy"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Lawrence Berkeley National Laboratory","raw_type":null}],"best_oa_location":{"id":"pmh:info:ark/67531/metadc877515","is_oa":true,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/","pdf_url":"https://digital.library.unt.edu/ark:/67531/metadc877515/m2/1/high_res_d/918549.pdf","source":{"id":"https://openalex.org/S4306400792","display_name":"University of North Texas Digital Library (University of North Texas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123534392","host_organization_name":"University of North Texas","host_organization_lineage":["https://openalex.org/I123534392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal Name: Society for Industrial and Applied Mathematics: Journal onMatrix Analysis and Applications; Journal Volume: 27; Journal Issue: 3; Related Information: Journal Publication Date: 2005","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1586068380.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1970716086","https://openalex.org/W1990238127","https://openalex.org/W2000582360","https://openalex.org/W2008017948","https://openalex.org/W2060931317","https://openalex.org/W2075865004","https://openalex.org/W2086987344","https://openalex.org/W2118357359","https://openalex.org/W2137541800","https://openalex.org/W2174300045","https://openalex.org/W2467346979","https://openalex.org/W4242722506"],"related_works":["https://openalex.org/W3176941588","https://openalex.org/W69588519","https://openalex.org/W2316741139","https://openalex.org/W3209452570","https://openalex.org/W1480331774","https://openalex.org/W1524137286","https://openalex.org/W2883427219","https://openalex.org/W2293219126","https://openalex.org/W3101473527","https://openalex.org/W1650849357","https://openalex.org/W2099853640","https://openalex.org/W3000858779","https://openalex.org/W43374781","https://openalex.org/W2793320699","https://openalex.org/W2298381282","https://openalex.org/W2952741639","https://openalex.org/W331571523","https://openalex.org/W2891084953","https://openalex.org/W3103979424","https://openalex.org/W2136347631"],"abstract_inverted_index":{"This":[0,71,184],"paper":[1],"is":[2,76,130,204],"concerned":[3],"with":[4,206],"solving":[5],"large-scale":[6],"eigenvalue":[7,222],"problems":[8],"by":[9,116],"algebraic":[10,55,67,212],"substructuring.":[11],"Algebraic":[12],"substructuring":[13,68,75,154,213],"refers":[14],"to":[15,25,45,49,78,169,187,218],"the":[16,50,79,127,137,146,156,159,170,178,226],"process":[17],"of":[18,38,66,74,96,113,136,148,158,161,163,200,230],"applying":[19],"matrix":[20,30,128,166],"reordering":[21,129],"and":[22,43,89,107,155],"partitioning":[23,135],"algorithms":[24],"divide":[26],"a":[27,36,63,133,164,188,202,220],"large":[28],"sparse":[29],"into":[31],"smaller":[32],"submatrices":[33],"from":[34,196,225],"which":[35,62],"subset":[37],"spectral":[39,193],"components":[40,160,194],"are":[41,182],"extracted":[42],"combined":[44],"form":[46],"approximate":[47,150],"solutions":[48],"original":[51,171],"problem.":[52,172],"Through":[53],"an":[54,142,149,231],"analysis,":[56],"we":[57],"identify":[58],"critical":[59],"conditions":[60],"under":[61],"simple":[64,189],"version":[65,73],"works":[69],"well.":[70],"particular":[72],"identical":[77],"component":[80],"mode":[81],"synthesis":[82],"(CMS)":[83],"method":[84],"(see":[85],"[R.":[86],"R.":[87],"Craig":[88],"M.":[90],"C.":[91,92,109],"Bampton,":[93],"{\\em":[94,111],"Coupling":[95],"substructures":[97],"for":[98,177,191],"dynamic":[99],"analysis},":[100],"AIAA":[101],"J.,":[102],"6":[103],"(1968),":[104],"pp.":[105,124],"1313--1319]":[106],"[W.":[108],"Hurty,":[110],"Vibrations":[112],"structure":[114],"systems":[115],"component-mode":[117],"synthesis},":[118],"J.":[119],"Engrg.":[120],"Mech.,":[121],"86":[122],"(1960),":[123],"51--69])":[125],"when":[126],"based":[131],"on":[132],"geometric":[134],"computational":[138],"domain.":[139],"We":[140,209],"observe":[141],"interesting":[143],"connection":[144],"between":[145],"accuracy":[147],"eigenpair":[151,180],"obtained":[152],"through":[153],"distribution":[157],"eigenvectors":[162],"canonical":[165],"pencil":[167],"congruent":[168],"A":[173],"priori":[174],"error":[175],"bounds":[176],"smallest":[179],"approximation":[181],"developed.":[183],"development":[185],"leads":[186],"heuristic":[190,203],"choosing":[192],"(modes)":[195],"each":[197],"substructure.The":[198],"effectiveness":[199],"such":[201],"demonstrated":[205],"numerical":[207],"examples.":[208],"show":[210],"that":[211],"can":[214],"be":[215],"effectively":[216],"used":[217],"solve":[219],"generalized":[221],"problem":[223],"arising":[224],"finite":[227],"element":[228],"analysis":[229],"accelerator":[232],"structure.":[233]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
