{"id":"https://openalex.org/W7134224609","doi":"https://doi.org/10.48550/arxiv.2603.05721","title":"FlexTrace: Exchangeable Randomized Trace Estimation for Matrix Functions","display_name":"FlexTrace: Exchangeable Randomized Trace Estimation for Matrix Functions","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134224609","doi":"https://doi.org/10.48550/arxiv.2603.05721"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.05721","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128465254","display_name":"Madhusudan Madhavan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Madhavan, Madhusudan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128581641","display_name":"Alen Alexanderian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexanderian, Alen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045561492","display_name":"Arvind K. Saibaba","orcid":"https://orcid.org/0000-0002-8698-6100"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saibaba, Arvind K.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7926999926567078,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7926999926567078,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.06310000270605087,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.026900000870227814,"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/trace","display_name":"TRACE (psycholinguistics)","score":0.8377000093460083},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6233000159263611},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49070000648498535},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4848000109195709},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.44269999861717224},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4359999895095825},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.41029998660087585}],"concepts":[{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.8377000093460083},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6233000159263611},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6031000018119812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5069000124931335},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49070000648498535},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4848000109195709},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44269999861717224},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4350999891757965},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41589999198913574},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.3736000061035156},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.36500000953674316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32089999318122864},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.2777999937534332}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.05721","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.05721","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.05721","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.05721","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,84],"consider":[1,85],"the":[2,6,45,86,111,133],"task":[3],"of":[4,8,15,114,132,135],"estimating":[5],"trace":[7,41,66,134],"a":[9,16,64],"matrix":[10,21,94],"function,":[11],"${\\rm":[12,75],"tr}(f({\\bf":[13,76],"A}))$,":[14],"large":[17],"symmetric":[18],"positive":[19],"semi-definite":[20],"${\\bf":[22,82],"A}$.":[23,83],"This":[24],"problem":[25],"arises":[26],"in":[27],"multiple":[28],"applications,":[29],"including":[30],"kernel":[31],"methods":[32,43],"and":[33,104,106,121],"inverse":[34],"problems.":[35],"A":[36],"key":[37],"challenge":[38],"across":[39,118],"existing":[40,140],"estimation":[42],"is":[44,90],"need":[46],"for":[47],"matrix-vector":[48],"products":[49],"(matvecs)":[50],"with":[51,81,96],"$f({\\bf":[52,136],"A})$,":[53],"which":[54,98],"can":[55],"be":[56],"very":[57],"expensive.":[58],"In":[59],"this":[60],"article,":[61],"we":[62],"introduce":[63],"novel":[65],"estimator,":[67],"FlexTrace,":[68],"an":[69,91],"exchangeable,":[70],"single-pass":[71],"method":[72],"that":[73,125],"estimates":[74,131],"A}))$":[77],"solely":[78],"using":[79],"matvecs":[80],"case":[87],"where":[88],"$f$":[89],"operator":[92],"monotone":[93],"function":[95],"$f(0)=0$,":[97],"includes":[99],"functions":[100],"such":[101],"as":[102],"$\\log(1+x)$":[103],"$x^{1/2}$,":[105],"derive":[107],"probabilistic":[108],"bounds":[109],"showcasing":[110],"theoretical":[112],"advantages":[113],"FlexTrace.":[115],"Numerical":[116],"experiments":[117],"synthetic":[119],"examples":[120],"application":[122],"domains":[123],"demonstrate":[124],"FlexTrace":[126],"provides":[127],"substantially":[128],"more":[129],"accurate":[130],"A})$":[137],"compared":[138],"to":[139],"methods.":[141]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2026-03-10T00:00:00"}
