{"id":"https://openalex.org/W2750001921","doi":"https://doi.org/10.1137/16m1078148","title":"Approximating Spectral Sums of Large-Scale Matrices using Stochastic Chebyshev Approximations","display_name":"Approximating Spectral Sums of Large-Scale Matrices using Stochastic Chebyshev Approximations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2750001921","doi":"https://doi.org/10.1137/16m1078148","mag":"2750001921"},"language":"en","primary_location":{"id":"doi:10.1137/16m1078148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1078148","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/A5082060594","display_name":"In\u2010Su Han","orcid":"https://orcid.org/0000-0001-9572-4076"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Insu Han","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026795227","display_name":"Dmitry Malioutov","orcid":"https://orcid.org/0000-0002-5541-7044"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dmitry Malioutov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072151198","display_name":"Haim Avron","orcid":"https://orcid.org/0000-0002-1688-9030"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haim Avron","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102928677","display_name":"Jinwoo Shin","orcid":"https://orcid.org/0000-0003-4313-4669"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinwoo Shin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082060594"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6805,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.95915904,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"39","issue":"4","first_page":"A1558","last_page":"A1585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10320","display_name":"Neural Networks and Applications","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.698034405708313},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48222243785858154},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.46501997113227844},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.44328904151916504},{"id":"https://openalex.org/keywords/trace-class","display_name":"Trace class","score":0.43875983357429504},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.4264930486679077},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42633044719696045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33769652247428894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2054339349269867},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.1187540590763092}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.698034405708313},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48222243785858154},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.46501997113227844},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.44328904151916504},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.43875983357429504},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.4264930486679077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42633044719696045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33769652247428894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2054339349269867},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.1187540590763092},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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:10.1137/16m1078148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1078148","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/G4297820378","display_name":null,"funder_award_id":"FA8750-12-C-0323","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W985544890","https://openalex.org/W1485063553","https://openalex.org/W1520053542","https://openalex.org/W1746819321","https://openalex.org/W1977463378","https://openalex.org/W1980130025","https://openalex.org/W1981115560","https://openalex.org/W1989751882","https://openalex.org/W1990457366","https://openalex.org/W1991085742","https://openalex.org/W1999174665","https://openalex.org/W2007755560","https://openalex.org/W2008389020","https://openalex.org/W2008697571","https://openalex.org/W2025970186","https://openalex.org/W2033672086","https://openalex.org/W2035080386","https://openalex.org/W2036977638","https://openalex.org/W2041735011","https://openalex.org/W2042782097","https://openalex.org/W2043994139","https://openalex.org/W2049766166","https://openalex.org/W2057450058","https://openalex.org/W2059998776","https://openalex.org/W2062087630","https://openalex.org/W2062388969","https://openalex.org/W2078480837","https://openalex.org/W2083057505","https://openalex.org/W2085276378","https://openalex.org/W2095999997","https://openalex.org/W2108214478","https://openalex.org/W2130152237","https://openalex.org/W2133396774","https://openalex.org/W2135912864","https://openalex.org/W2154812977","https://openalex.org/W2169495281","https://openalex.org/W2171317928","https://openalex.org/W2547245280","https://openalex.org/W2964321151","https://openalex.org/W3104200791","https://openalex.org/W3105113144"],"related_works":["https://openalex.org/W2316482036","https://openalex.org/W2269060792","https://openalex.org/W2163737695","https://openalex.org/W2006016949","https://openalex.org/W287675216","https://openalex.org/W1986293006","https://openalex.org/W2032822277","https://openalex.org/W2768943341","https://openalex.org/W4306920661","https://openalex.org/W2382785608"],"abstract_inverted_index":{"Computation":[0],"of":[1,4,53,56,90,100,113,117,150,174],"the":[2,51,85,88,98,101,104,114,118,122,128],"trace":[3,52,73,149],"a":[5,39,45,91,95],"matrix":[6,54,102,145,151],"function":[7,66,92,129],"plays":[8],"an":[9],"important":[10,144],"role":[11],"in":[12,19,87,111],"many":[13],"scientific":[14],"computing":[15],"applications,":[16],"including":[17,147],"applications":[18],"machine":[20],"learning,":[21],"computational":[22,31],"physics":[23],"(e.g.,":[24,33],"lattice":[25],"quantum":[26],"chromodynamics),":[27],"network":[28],"analysis,":[29],"and":[30,77,103,121,157,166],"biology":[32],"protein":[34],"folding),":[35],"just":[36],"to":[37,84,97,127],"name":[38],"few":[40],"application":[41],"areas.":[42],"We":[43,106,161],"propose":[44],"linear-time":[46],"randomized":[47],"algorithm":[48,61,165],"for":[49,143],"approximating":[50],"functions":[55],"large":[57],"symmetric":[58],"matrices.":[59],"Our":[60],"is":[62],"based":[63],"on":[64,133,170],"coupling":[65],"approximation":[67,109],"using":[68],"Chebyshev":[69],"interpolation":[70],"with":[71,140,172],"stochastic":[72],"estimators":[74],"(Hutchinson's":[75],"method),":[76],"as":[78],"such":[79],"requires":[80],"only":[81],"implicit":[82],"access":[83],"matrix,":[86,120],"form":[89],"that":[93,125],"maps":[94],"vector":[96],"product":[99],"vector.":[105],"provide":[107,138],"rigorous":[108],"error":[110],"terms":[112],"extremal":[115],"eigenvalue":[116],"input":[119],"Bernstein":[123],"ellipse":[124],"corresponds":[126],"at":[130],"hand.":[131],"Based":[132],"our":[134,164],"general":[135],"scheme,":[136],"we":[137],"algorithms":[139],"provable":[141],"guarantees":[142],"computations,":[146],"log-determinant,":[148],"inverse,":[152],"Estrada":[153],"index,":[154],"Schatten":[155],"$p$-norm,":[156],"testing":[158],"positive":[159],"definiteness.":[160],"experimentally":[162],"evaluate":[163],"demonstrate":[167],"its":[168],"effectiveness":[169],"matrices":[171],"tens":[173],"millions":[175],"dimensions.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}