{"id":"https://openalex.org/W2481831657","doi":"https://doi.org/10.1137/16m1056481","title":"Convergence Analysis of Restarted Krylov Subspace Eigensolvers","display_name":"Convergence Analysis of Restarted Krylov Subspace Eigensolvers","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2481831657","doi":"https://doi.org/10.1137/16m1056481","mag":"2481831657"},"language":"en","primary_location":{"id":"doi:10.1137/16m1056481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1056481","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/A5012778133","display_name":"Klaus Neymeyr","orcid":"https://orcid.org/0000-0002-1464-2851"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Klaus Neymeyr","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028066219","display_name":"Ming Zhou","orcid":"https://orcid.org/0000-0001-7096-1649"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ming Zhou","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012778133"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6969,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74588851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"37","issue":"3","first_page":"955","last_page":"975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9909999966621399,"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/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.8104099035263062},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8056524991989136},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.802318811416626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7756003737449646},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7261179089546204},{"id":"https://openalex.org/keywords/rayleigh-quotient-iteration","display_name":"Rayleigh quotient iteration","score":0.7132890224456787},{"id":"https://openalex.org/keywords/ritz-method","display_name":"Ritz method","score":0.6360818147659302},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6278462409973145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5940371155738831},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.564389705657959},{"id":"https://openalex.org/keywords/rayleigh\u2013ritz-method","display_name":"Rayleigh\u2013Ritz method","score":0.5516124367713928},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5166947841644287},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.42099684476852417},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3616315722465515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28561240434646606},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23591506481170654},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1908566951751709},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.14739269018173218},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.0596175491809845}],"concepts":[{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.8104099035263062},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8056524991989136},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.802318811416626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7756003737449646},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7261179089546204},{"id":"https://openalex.org/C117586675","wikidata":"https://www.wikidata.org/wiki/Q7298489","display_name":"Rayleigh quotient iteration","level":4,"score":0.7132890224456787},{"id":"https://openalex.org/C21575042","wikidata":"https://www.wikidata.org/wiki/Q905132","display_name":"Ritz method","level":3,"score":0.6360818147659302},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6278462409973145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5940371155738831},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.564389705657959},{"id":"https://openalex.org/C70940138","wikidata":"https://www.wikidata.org/wiki/Q852247","display_name":"Rayleigh\u2013Ritz method","level":3,"score":0.5516124367713928},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5166947841644287},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.42099684476852417},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3616315722465515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28561240434646606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23591506481170654},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1908566951751709},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.14739269018173218},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0596175491809845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1056481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1056481","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W597568752","https://openalex.org/W1522512418","https://openalex.org/W1522703524","https://openalex.org/W1966236905","https://openalex.org/W1974907720","https://openalex.org/W1976798627","https://openalex.org/W1981308866","https://openalex.org/W2012728721","https://openalex.org/W2027436456","https://openalex.org/W2037034729","https://openalex.org/W2059586807","https://openalex.org/W2066910699","https://openalex.org/W2109443444","https://openalex.org/W2141193768","https://openalex.org/W2148173888","https://openalex.org/W2163343060","https://openalex.org/W2342748186","https://openalex.org/W2350991510","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W4283689117","https://openalex.org/W4383645627","https://openalex.org/W4297437581","https://openalex.org/W4323927193","https://openalex.org/W2140314231","https://openalex.org/W2017959572","https://openalex.org/W2909714470","https://openalex.org/W2978804717","https://openalex.org/W4236978178","https://openalex.org/W2185877463"],"abstract_inverted_index":{"The":[0,28,80,103],"$A$-gradient":[1,29],"minimization":[2,69],"of":[3,37,62,70,77,96],"the":[4,16,34,45,68,71,84,88,97,100,122],"Rayleigh":[5,72],"quotient":[6,73],"allows":[7],"one":[8],"to":[9],"construct":[10],"robust":[11],"and":[12,24,87,133,143,154],"fast-convergent":[13],"eigensolvers":[14],"for":[15,20,44,67],"generalized":[17],"eigenvalue":[18],"problem":[19],"$(A,M)$":[21],"with":[22,74,114],"symmetric":[23],"positive":[25],"definite":[26],"matrices.":[27],"steepest":[30],"descent":[31],"iteration":[32,98],"is":[33],"simplest":[35],"case":[36,47],"more":[38],"general":[39],"restarted":[40,63],"Krylov":[41,52,64,75],"subspace":[42,65],"iterations":[43,66],"special":[46],"that":[48],"all":[49],"stepwise":[50],"generated":[51],"subspaces":[53,76],"are":[54,91],"two-dimensional.":[55],"This":[56],"paper":[57],"contains":[58],"a":[59,108,115,156],"convergence":[60,105],"analysis":[61,106],"arbitrary":[78],"dimensions.":[79],"eigenpair":[81],"approximations,":[82],"namely,":[83],"Ritz":[85,89,110,116],"vector":[86,111],"value,":[90],"extracted":[92],"in":[93],"each":[94],"step":[95],"by":[99,125],"Rayleigh--Ritz":[101],"procedure.":[102],"new":[104],"provides":[107],"sharp":[109],"estimate":[112],"together":[113],"value":[117],"estimate.":[118],"These":[119],"results":[120],"improve":[121],"classical":[123],"estimates":[124],"Kaniel":[126],"[Math.":[127],"Comp.,":[128],"20":[129],"(1966),":[130],"pp.":[131,141,168],"369--378]":[132],"Saad":[134],"[SIAM":[135],"J.":[136,161],"Numer.":[137,162],"Anal.,":[138],"17":[139],"(1980),":[140],"687--706]":[142],"Parlett":[144],"[The":[145],"Symmetric":[146],"Eigenvalue":[147],"Problem,":[148],"Prentice-Hall,":[149],"Englewood":[150],"Cliffs,":[151],"NJ,":[152],"1980]":[153],"generalize":[155],"result":[157],"from":[158],"Knyazev":[159],"[Russian":[160],"Anal.":[163],"Math.":[164],"Modelling,":[165],"2":[166],"(1987),":[167],"371--396].":[169]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
