{"id":"https://openalex.org/W2065931256","doi":"https://doi.org/10.1137/080733383","title":"A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices","display_name":"A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2065931256","doi":"https://doi.org/10.1137/080733383","mag":"2065931256"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/080733383","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0906.2242","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075378610","display_name":"Zhongxiao Jia","orcid":"https://orcid.org/0000-0001-9761-8517"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhongxiao Jia","raw_affiliation_strings":["jiazx@tsinghua.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"jiazx@tsinghua.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008984643","display_name":"Datian Niu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Datian Niu","raw_affiliation_strings":["niudt@dlnu.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"niudt@dlnu.edu.cn#TAB#","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.359,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":46,"citation_normalized_percentile":{"value":0.972309,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":95},"biblio":{"volume":"32","issue":"2","first_page":"714","last_page":"744"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9999,"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":0.9999,"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":0.9904,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9816,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.5615034},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.47889724},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4205673},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.41358912}],"concepts":[{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.87262535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817068},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6830348},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.57655245},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.5615034},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.47889724},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.44996732},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4358586},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4205673},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.41358912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36565733},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23041445},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16897169},{"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},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/080733383","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0906.2242","pdf_url":"https://arxiv.org/pdf/0906.2242","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.2242","pdf_url":"http://arxiv.org/pdf/0906.2242","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/0906.2242","pdf_url":"https://arxiv.org/pdf/0906.2242","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":33,"referenced_works":["https://openalex.org/W1522512418","https://openalex.org/W1562237811","https://openalex.org/W1596181878","https://openalex.org/W1965497533","https://openalex.org/W1965855526","https://openalex.org/W1975109850","https://openalex.org/W1977271024","https://openalex.org/W1977361006","https://openalex.org/W1981745143","https://openalex.org/W2006651457","https://openalex.org/W2010315317","https://openalex.org/W2017895259","https://openalex.org/W2021710646","https://openalex.org/W2030827135","https://openalex.org/W2034775820","https://openalex.org/W2047811252","https://openalex.org/W2059586807","https://openalex.org/W2064559422","https://openalex.org/W2069262775","https://openalex.org/W2073955633","https://openalex.org/W2074095860","https://openalex.org/W2075511500","https://openalex.org/W2087549321","https://openalex.org/W2091138132","https://openalex.org/W2094371111","https://openalex.org/W2104802194","https://openalex.org/W2136537636","https://openalex.org/W2154202969","https://openalex.org/W2158495995","https://openalex.org/W2183009162","https://openalex.org/W2342316458","https://openalex.org/W2798909945","https://openalex.org/W749579920"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W3176451595","https://openalex.org/W2654090051","https://openalex.org/W2156009096","https://openalex.org/W2073696440","https://openalex.org/W2058241770","https://openalex.org/W2027838537","https://openalex.org/W2013186713","https://openalex.org/W1980579360","https://openalex.org/W1970812947"],"abstract_inverted_index":{"The":[0,135],"harmonic":[1,27,44,63,94,105,122,162,181,189,196,212],"Lanczos":[2,95,163,197,231],"bidiagonalization":[3,96,164,198,232],"method":[4,97],"can":[5,207,245],"be":[6,246],"used":[7,191],"to":[8,73,86,140,142,172],"compute":[9,209],"the":[10,32,41,54,77,87,100,104,114,120,126,130,143,148,154,174,188,193,210,230,252],"smallest":[11,253],"singular":[12,51,110,117,145,254],"triplets":[13],"of":[14,34,56,103,132],"a":[15,92,203],"large":[16,82],"matrix":[17,83],"A.":[18],"We":[19,169,201],"prove":[20],"that":[21,98,183,206,221,236],"for":[22,81],"good":[23,152],"enough":[24],"projection":[25,79],"subspaces":[26,128,149],"Ritz":[28,45,64,106,123],"values":[29,46,52,111],"converge":[30,67,141],"if":[31],"columns":[33,55],"A":[35,57],"are":[36,58,138,150,184,219],"strongly":[37],"linearly":[38,60],"independent.":[39],"On":[40],"other":[42,226],"hand,":[43],"may":[47,66,70],"miss":[48],"some":[49],"desired":[50,144],"when":[53,250],"almost":[59],"dependent.":[61],"Furthermore,":[62],"vectors":[65,107,146],"irregularly":[68],"and":[69,112,153,178,215,244],"even":[71],"fail":[72],"converge.":[74,157],"Based":[75],"on":[76,229],"refined":[78,93,121,136,161,180,211],"principle":[80],"eigenproblems":[84],"due":[85],"first":[88],"author,":[89],"we":[90],"propose":[91,202],"takes":[99],"Rayleigh":[101,155],"quotients":[102,156],"as":[108],"approximate":[109,116],"extracts":[113],"best":[115,175],"vectors,":[118],"called":[119],"approximations,":[124],"from":[125],"given":[127],"in":[129],"sense":[131],"residual":[133],"minimizations.":[134],"approximations":[137],"shown":[139],"once":[147],"sufficiently":[151],"An":[158],"implicitly":[159,194],"restarted":[160,195],"algorithm":[165,199],"(IRRHLB)":[166],"is":[167,238],"developed.":[168],"study":[170],"how":[171],"select":[173],"possible":[176],"shifts,":[177],"suggest":[179],"shifts":[182,190,213],"theoretically":[185],"better":[186],"than":[187],"within":[192],"(IRHLB).":[200],"novel":[204],"procedure":[205],"numerically":[208],"efficiently":[214],"accurately.":[216],"Numerical":[217],"experiments":[218],"reported":[220],"compare":[222],"IRRHLB":[223,237],"with":[224,242],"five":[225],"algorithms":[227],"based":[228],"process.":[233],"It":[234],"appears":[235],"at":[239],"least":[240],"competitive":[241],"them":[243],"considerably":[247],"more":[248],"efficient":[249],"computing":[251],"triplets.":[255]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2065931256","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-03-23T10:37:37.607097","created_date":"2016-06-24"}