{"id":"https://openalex.org/W2964114051","doi":"https://doi.org/10.1002/nla.2170","title":"A posteriori error estimate for computing tr( f ( A )) by using the Lanczos method","display_name":"A posteriori error estimate for computing tr( f ( A )) by using the Lanczos method","publication_year":2018,"publication_date":"2018-03-14","ids":{"openalex":"https://openalex.org/W2964114051","doi":"https://doi.org/10.1002/nla.2170","mag":"2964114051"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2170","pdf_url":"https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1002/nla.2170","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1002/nla.2170","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010479652","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0003-4599-3600"},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jie Chen","raw_affiliation_string":"[IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA]","raw_affiliation_strings":["[IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA]"]},{"author_position":"last","author":{"id":"https://openalex.org/A5016419713","display_name":"Yousef Saad","orcid":"https://orcid.org/0000-0002-8614-5360"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516","https://openalex.org/I2800403580"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yousef Saad","raw_affiliation_string":"Department of Computer Science and Engineering University of Minnesota Twin Cities Minneapolis USA","raw_affiliation_strings":["Department of Computer Science and Engineering University of Minnesota Twin Cities Minneapolis USA"]}],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010479652"],"corresponding_institution_ids":["https://openalex.org/I4210114115"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"apc_paid":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"cited_by_percentile_year":{"min":81,"max":82},"biblio":{"volume":"25","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Algorithms and Iterative Methods","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 Algorithms and Iterative Methods","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/T13487","display_name":"Total Least Squares Methods and Applications","score":0.996,"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"}},{"id":"https://openalex.org/T10963","display_name":"Numerical Optimization Techniques","score":0.9939,"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":[{"keyword":"posteriori error estimate","score":0.5261},{"keyword":"tr","score":0.3221}],"concepts":[{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.687273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.65543723},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.6131524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.61275965},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.60624146},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5604627},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.45090312},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.44819677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42420956},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41024002},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32881838},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.21918243},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13786966},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials 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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2170","pdf_url":"https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1002/nla.2170","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2170","pdf_url":"https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1002/nla.2170","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation","award_id":"CCF-1318597"}],"referenced_works_count":33,"referenced_works":["https://openalex.org/W55912154","https://openalex.org/W603018635","https://openalex.org/W648869842","https://openalex.org/W985544890","https://openalex.org/W1491884104","https://openalex.org/W1506342804","https://openalex.org/W1510593638","https://openalex.org/W1711916224","https://openalex.org/W1990457366","https://openalex.org/W1996865144","https://openalex.org/W2020328455","https://openalex.org/W2035864055","https://openalex.org/W2038273756","https://openalex.org/W2040600273","https://openalex.org/W2055373329","https://openalex.org/W2057450058","https://openalex.org/W2057602562","https://openalex.org/W2062388969","https://openalex.org/W2078685623","https://openalex.org/W2081060015","https://openalex.org/W2091922944","https://openalex.org/W2108214478","https://openalex.org/W2130152237","https://openalex.org/W2137636417","https://openalex.org/W2138249740","https://openalex.org/W2217466820","https://openalex.org/W2540972713","https://openalex.org/W2547245280","https://openalex.org/W2963762865","https://openalex.org/W2964321151","https://openalex.org/W3098944298","https://openalex.org/W3104200791","https://openalex.org/W3105113144"],"related_works":["https://openalex.org/W2120665288","https://openalex.org/W2035084401","https://openalex.org/W1601294834","https://openalex.org/W2082058757","https://openalex.org/W2170044215","https://openalex.org/W1990972291","https://openalex.org/W591632009","https://openalex.org/W2093966383","https://openalex.org/W1982342918","https://openalex.org/W1973379861"],"ngrams_url":"https://api.openalex.org/works/W2964114051/ngrams","abstract_inverted_index":{"Summary":[0],"An":[1],"outstanding":[2],"problem":[3,93,124],"when":[4,25],"computing":[5,96,126],"a":[6,9,17,87,91,99,133,211,226,230,241],"function":[7,36],"of":[8,33,56,90,101,104,112,125,169,179,196,199,210,222,232,236],"matrix,":[10],"f":[11,64,82,128,157,170],"(":[12,65,83,129,158,171],"A":[13,66,84,130,137,159,172],"),":[14],"by":[15,138],"using":[16,139],"Krylov":[18],"method":[19,142],"is":[20,27,60,86,108,116,194],"to":[21,50,81,239],"accurately":[22],"estimate":[23,150,165,193],"errors":[24],"convergence":[26],"slow.":[28],"Apart":[29],"from":[30],"the":[31,34,43,51,54,62,71,78,102,110,113,123,140,152,167,176,190,197,207,220,234],"case":[32],"exponential":[35],"that":[37,109,189],"has":[38],"been":[39],"extensively":[40],"studied":[41],"in":[42,58,186,214],"past,":[44],"there":[45],"are":[46],"no":[47],"well\u2010established":[48],"solutions":[49],"problem.":[52],"Often,":[53],"quantity":[55],"interest":[57],"applications":[59],"not":[61],"matrix":[63,136,213],")":[67,85,160],"itself":[68],"but":[69],"rather":[70],"matrix\u2013vector":[72],"products":[73],"or":[74],"bilinear":[75,153],"forms.":[76],"When":[77],"computation":[79],"related":[80],"building":[88],"block":[89],"larger":[92],"(e.g.,":[94],"approximately":[95],"its":[97],"trace),":[98],"consequence":[100],"lack":[103],"reliable":[105],"error":[106,149,164,192,223],"estimates":[107,181],"accuracy":[111],"computed":[114],"result":[115],"unknown.":[117],"In":[118],"this":[119],"paper,":[120],"we":[121,205],"consider":[122],"tr(":[127],"))":[131],"for":[132,151,166,182],"symmetric":[134],"positive\u2010definite":[135],"Lanczos":[141,237],"and":[143,161,218],"make":[144],"two":[145],"contributions:":[146],"(a)":[147],"an":[148,163,203],"form":[154],"associated":[155],"with":[156],"(b)":[162],"trace":[168,191],").":[173],"We":[174],"demonstrate":[175],"practical":[177],"usefulness":[178],"these":[180],"large":[183],"matrices":[184],"and,":[185],"particular,":[187],"show":[188],"indicative":[195],"number":[198,235],"accurate":[200],"digits.":[201],"As":[202],"application,":[204],"compute":[206],"log":[208],"determinant":[209],"covariance":[212],"Gaussian":[215],"process":[216],"analysis":[217],"underline":[219],"importance":[221],"tolerance":[224],"as":[225,229],"stopping":[227],"criterion":[228],"means":[231],"bounding":[233],"steps":[238],"achieve":[240],"desired":[242],"accuracy.":[243]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2964114051","counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2024-03-02T19:24:28.826918","created_date":"2019-07-30"}