{"id":"https://openalex.org/W1980431326","doi":"https://doi.org/10.1137/s0895479895281484","title":"Deflation Techniques for an Implicitly Restarted Arnoldi Iteration","display_name":"Deflation Techniques for an Implicitly Restarted Arnoldi Iteration","publication_year":1996,"publication_date":"1996-10-01","ids":{"openalex":"https://openalex.org/W1980431326","doi":"https://doi.org/10.1137/s0895479895281484","mag":"1980431326"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479895281484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895281484","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5057121475","display_name":"Richard B. Lehoucq","orcid":"https://orcid.org/0000-0003-2579-1374"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. B. Lehoucq","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109866106","display_name":"D. C. Sorensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. C. Sorensen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057121475"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2775,"has_fulltext":false,"cited_by_count":622,"citation_normalized_percentile":{"value":0.98371423,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"17","issue":"4","first_page":"789","last_page":"821"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.7610195875167847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.741284966468811},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.739086389541626},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7006386518478394},{"id":"https://openalex.org/keywords/ritz-method","display_name":"Ritz method","score":0.6467742323875427},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6304271817207336},{"id":"https://openalex.org/keywords/deflation","display_name":"Deflation","score":0.6295962333679199},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.6242678165435791},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5898852348327637},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5115090608596802},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4825103282928467},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.4723026752471924},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.46540218591690063},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4205366373062134},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4178754687309265},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3521045446395874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20973432064056396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17896413803100586},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.0681314766407013},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06420955061912537}],"concepts":[{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.7610195875167847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741284966468811},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.739086389541626},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7006386518478394},{"id":"https://openalex.org/C21575042","wikidata":"https://www.wikidata.org/wiki/Q905132","display_name":"Ritz method","level":3,"score":0.6467742323875427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6304271817207336},{"id":"https://openalex.org/C8112001","wikidata":"https://www.wikidata.org/wiki/Q161081","display_name":"Deflation","level":3,"score":0.6295962333679199},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.6242678165435791},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5898852348327637},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5115090608596802},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4825103282928467},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.4723026752471924},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.46540218591690063},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4205366373062134},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4178754687309265},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3521045446395874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20973432064056396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17896413803100586},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0681314766407013},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06420955061912537},{"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/C126285488","wikidata":"https://www.wikidata.org/wiki/Q178476","display_name":"Monetary policy","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0895479895281484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895281484","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:ADA447560","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA447560","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.9911","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.9911","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.caam.rice.edu/pub/software/ARPACK/DOCS/lockpg.ps.gz","raw_type":"text"},{"id":"pmh:oai:scholarship.rice.edu:1911/101832","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/101832","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W101236918","https://openalex.org/W141418607","https://openalex.org/W1522703524","https://openalex.org/W1563653928","https://openalex.org/W1668492065","https://openalex.org/W1966430299","https://openalex.org/W1984536994","https://openalex.org/W1986951886","https://openalex.org/W1990238127","https://openalex.org/W2000537011","https://openalex.org/W2005752655","https://openalex.org/W2008694421","https://openalex.org/W2037620736","https://openalex.org/W2040608867","https://openalex.org/W2048659456","https://openalex.org/W2054689585","https://openalex.org/W2063375366","https://openalex.org/W2065304525","https://openalex.org/W2069262775","https://openalex.org/W2069281158","https://openalex.org/W2070984764","https://openalex.org/W2080634148","https://openalex.org/W2086625748","https://openalex.org/W2088748973","https://openalex.org/W2106869373","https://openalex.org/W2117686912","https://openalex.org/W2565470101","https://openalex.org/W4251656402"],"related_works":["https://openalex.org/W2015942935","https://openalex.org/W3134028852","https://openalex.org/W2037894849","https://openalex.org/W2804908571","https://openalex.org/W2227692226","https://openalex.org/W2169765983","https://openalex.org/W2034236710","https://openalex.org/W2058557317","https://openalex.org/W1999476674","https://openalex.org/W2921642051"],"abstract_inverted_index":{"A":[0,42,127],"deflation":[1,110],"procedure":[2],"is":[3,6,46,98,106,130],"introduced":[4,47],"that":[5,48],"designed":[7],"to":[8,115,139],"improve":[9],"the":[10,28,31,36,51,55,77,81,96],"convergence":[11],"of":[12,23,35,61,80,95],"an":[13],"implicitly":[14,49],"restarted":[15],"Arnoldi":[16],"iteration":[17,29,97],"for":[18],"computing":[19],"a":[20,24,66,85,101,122],"few":[21],"eigenvalues":[22,37,120],"large":[25],"matrix.":[26],"As":[27],"progresses,":[30],"Ritz":[32,71,92],"value":[33],"approximations":[34,53],"converge":[38],"at":[39],"different":[40],"rates.":[41],"numerically":[43],"stable":[44],"scheme":[45],"deflates":[50],"converged":[52,70,91],"from":[54,76],"iteration.":[56,82],"We":[57],"present":[58],"two":[59],"forms":[60],"implicit":[62],"deflation.":[63],"The":[64,83,109],"first,":[65],"locking":[67],"operation,":[68,87],"decouples":[69],"values":[72],"and":[73,100,142],"associated":[74],"vectors":[75],"active":[78],"part":[79],"second,":[84],"purging":[86],"removes":[88],"unwanted":[89],"but":[90],"pairs.":[93],"Convergence":[94],"improved":[99],"reduction":[102],"in":[103],"computational":[104,143],"effort":[105],"also":[107],"achieved.":[108],"strategies":[111],"make":[112],"it":[113],"possible":[114],"compute":[116],"multiple":[117],"or":[118],"clustered":[119],"with":[121,137],"single":[123],"vector":[124],"restart":[125],"method.":[126],"block":[128],"method":[129],"not":[131],"required.":[132],"These":[133],"schemes":[134],"are":[135,145],"analyzed":[136],"respect":[138],"numerical":[140],"stability,":[141],"results":[144],"presented.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":33},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":44},{"year":2018,"cited_by_count":32},{"year":2017,"cited_by_count":32},{"year":2016,"cited_by_count":45},{"year":2015,"cited_by_count":38},{"year":2014,"cited_by_count":32},{"year":2013,"cited_by_count":36},{"year":2012,"cited_by_count":34}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}