{"id":"https://openalex.org/W4296686646","doi":"https://doi.org/10.1137/21m1438633","title":"SuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured Matrices","display_name":"SuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured Matrices","publication_year":2022,"publication_date":"2022-09-22","ids":{"openalex":"https://openalex.org/W4296686646","doi":"https://doi.org/10.1137/21m1438633"},"language":"en","primary_location":{"id":"doi:10.1137/21m1438633","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1438633","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049118196","display_name":"Xiaofeng Ou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaofeng Ou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047496441","display_name":"Jianlin Xia","orcid":"https://orcid.org/0000-0002-9653-9312"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianlin Xia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4366,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81153816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"44","issue":"5","first_page":"A3041","last_page":"A3066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9951000213623047,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9887999892234802,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7931766510009766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6992652416229248},{"id":"https://openalex.org/keywords/divide-and-conquer-algorithms","display_name":"Divide and conquer algorithms","score":0.6817230582237244},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.6182432770729065},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.506414532661438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46336671710014343},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46275612711906433},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4602545499801636},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.41838616132736206},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4101071357727051},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3663572669029236},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21442767977714539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18190670013427734}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7931766510009766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6992652416229248},{"id":"https://openalex.org/C71559656","wikidata":"https://www.wikidata.org/wiki/Q671298","display_name":"Divide and conquer algorithms","level":2,"score":0.6817230582237244},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.6182432770729065},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.506414532661438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46336671710014343},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46275612711906433},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4602545499801636},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.41838616132736206},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4101071357727051},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3663572669029236},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21442767977714539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18190670013427734},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1438633","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1438633","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G512325790","display_name":null,"funder_award_id":"DMS-1819166","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W79284254","https://openalex.org/W1584657480","https://openalex.org/W1969313170","https://openalex.org/W1973915465","https://openalex.org/W1976998625","https://openalex.org/W1983103429","https://openalex.org/W1984265227","https://openalex.org/W1997345811","https://openalex.org/W2006399983","https://openalex.org/W2010464263","https://openalex.org/W2017641901","https://openalex.org/W2018419001","https://openalex.org/W2029837479","https://openalex.org/W2036403858","https://openalex.org/W2058221770","https://openalex.org/W2060410460","https://openalex.org/W2060492405","https://openalex.org/W2069914477","https://openalex.org/W2071077570","https://openalex.org/W2072396164","https://openalex.org/W2075490698","https://openalex.org/W2083095625","https://openalex.org/W2083206954","https://openalex.org/W2083903752","https://openalex.org/W2089958289","https://openalex.org/W2105433369","https://openalex.org/W2105591391","https://openalex.org/W2114583457","https://openalex.org/W2133549820","https://openalex.org/W2138106543","https://openalex.org/W2141719776","https://openalex.org/W2160774872","https://openalex.org/W2188296733","https://openalex.org/W2229505215","https://openalex.org/W2329958935","https://openalex.org/W2347093389","https://openalex.org/W2523571399","https://openalex.org/W2542454984","https://openalex.org/W3044852522","https://openalex.org/W3135719692","https://openalex.org/W3160944730","https://openalex.org/W3203168160","https://openalex.org/W4229666556","https://openalex.org/W4294988936","https://openalex.org/W4298876968","https://openalex.org/W4300681438","https://openalex.org/W4301491118","https://openalex.org/W4320800818"],"related_works":["https://openalex.org/W2352794675","https://openalex.org/W1539994214","https://openalex.org/W2051228988","https://openalex.org/W4247094814","https://openalex.org/W108531593","https://openalex.org/W2111712077","https://openalex.org/W1968151527","https://openalex.org/W3174042135","https://openalex.org/W2758927197","https://openalex.org/W2768528669"],"abstract_inverted_index":{"For":[0],"dense":[1],"symmetric":[2],"matrices":[3],"with":[4,21,65,84,104,185],"small":[5],"off-diagonal":[6],"(numerical)":[7],"ranks":[8,96],"and":[9,92,133,176,189,230],"in":[10,34,50],"a":[11,17,78,139,154,182,186,191],"hierarchically":[12],"semiseparable":[13],"form,":[14],"we":[15,76,137,152],"give":[16,77,190],"divide-and-conquer":[18],"eigendecomposition":[19],"method":[20,118],"nearly":[22,212],"linear":[23,213],"complexity":[24,214],"(called":[25],"SuperDC)":[26],"that":[27,86],"significantly":[28,206],"improves":[29],"an":[30],"earlier":[31],"basic":[32],"algorithm":[33,53,111],"[J.":[35],"Vogel,":[36],"et":[37],"al.,":[38],"SIAM":[39],"J.":[40],"Sci.":[41],"Comput.,":[42],"38":[43],"(2016),":[44],"PP.":[45],"A1358--A1382].":[46],"Some":[47],"stability":[48,208],"risks":[49,127],"the":[51,73,88,95,101,109,114,126,164,174,177,195,198,211,217,228],"original":[52,110],"are":[54,148,224],"analyzed,":[55],"including":[56],"potential":[57],"exponential":[58,89],"norm":[59,90],"growth,":[60],"cancellations,":[61],"loss":[62],"of":[63,97,128,166,194,197,232],"accuracy":[64,231],"clustered":[66,149],"eigenvalues":[67],"or":[68],"intermediate":[69,150],"eigenvalues,":[70,151],"etc.":[71],"In":[72,100],"dividing":[74],"stage,":[75],"new":[79],"structured":[80],"low-rank":[81,98,105],"updating":[82],"strategy":[83,158,184],"balancing":[85],"eliminates":[87],"growth":[91],"also":[93,180],"minimizes":[94],"updates.":[99],"conquering":[102],"stage":[103],"updated":[106],"eigenvalue":[107,219],"solution,":[108],"directly":[112],"uses":[113],"standard":[115],"fast":[116],"multipole":[117],"(FMM)":[119],"to":[120,142,159,226],"accelerate":[121],"function":[122],"evaluations,":[123],"which":[124],"has":[125,205],"cancellation,":[129],"division":[130],"by":[131],"zero,":[132],"slow":[134],"convergence.":[135],"Here,":[136],"design":[138,153],"triangular":[140],"FMM":[141,161],"avoid":[143],"cancellation.":[144],"Furthermore,":[145],"when":[146],"there":[147],"novel":[155],"local":[156],"shifting":[157],"integrate":[160],"accelerations":[162],"into":[163],"solution":[165],"shifted":[167],"secular":[168],"equations.":[169],"This":[170],"helps":[171],"achieve":[172],"both":[173],"efficiency":[175,229],"reliability.":[178],"We":[179],"provide":[181],"deflation":[183],"user-supplied":[187],"tolerance":[188],"precise":[192],"description":[193],"structure":[196],"resulting":[199],"eigenvector":[200],"matrix.":[201],"The":[202],"SuperDC":[203],"eigensolver":[204],"improved":[207],"while":[209],"keeping":[210],"for":[215],"finding":[216],"entire":[218],"decomposition.":[220],"Extensive":[221],"numerical":[222],"tests":[223],"used":[225],"show":[227],"SuperDC.":[233]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
