{"id":"https://openalex.org/W4323656955","doi":"https://doi.org/10.1137/22m1476277","title":"Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix","display_name":"Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix","publication_year":2023,"publication_date":"2023-03-09","ids":{"openalex":"https://openalex.org/W4323656955","doi":"https://doi.org/10.1137/22m1476277"},"language":"en","primary_location":{"id":"doi:10.1137/22m1476277","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1476277","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/A5081221153","display_name":"Eric Hallman","orcid":"https://orcid.org/0000-0001-7908-2296"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eric Hallman","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA"],"raw_orcid":"https://orcid.org/0000-0001-7908-2296","affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036959652","display_name":"Ilse C. F. Ipsen","orcid":"https://orcid.org/0000-0001-5645-5854"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilse C. F. Ipsen","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA"],"raw_orcid":"https://orcid.org/0000-0001-5645-5854","affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045561492","display_name":"Arvind K. Saibaba","orcid":"https://orcid.org/0000-0002-8698-6100"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arvind K. Saibaba","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA"],"raw_orcid":"https://orcid.org/0000-0002-8698-6100","affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081221153"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":1.3173,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80110096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"44","issue":"1","first_page":"240","last_page":"269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.998199999332428,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6784601211547852},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.632780909538269},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6005480289459229},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49532046914100647},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4867153465747833},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47504687309265137},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.43806716799736023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43797656893730164},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.42277902364730835},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18463438749313354}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784601211547852},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.632780909538269},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6005480289459229},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49532046914100647},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4867153465747833},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47504687309265137},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.43806716799736023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43797656893730164},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.42277902364730835},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18463438749313354},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1476277","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1476277","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":[{"id":"https://openalex.org/G4430187017","display_name":null,"funder_award_id":"DMS-1845406","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4786191534","display_name":null,"funder_award_id":"DMS-1760374","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4992198495","display_name":null,"funder_award_id":"DE-SC0022085","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G969983811","display_name":null,"funder_award_id":"DMS-1745654","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W2007755560","https://openalex.org/W2037757210","https://openalex.org/W2043310665","https://openalex.org/W2057450058","https://openalex.org/W2087338340","https://openalex.org/W2089181240","https://openalex.org/W2108214478","https://openalex.org/W2144164089","https://openalex.org/W2890517610","https://openalex.org/W2963482218","https://openalex.org/W3014220515","https://openalex.org/W3086898416","https://openalex.org/W3102600984","https://openalex.org/W4206039841","https://openalex.org/W4211094263","https://openalex.org/W4244155866","https://openalex.org/W4250954493","https://openalex.org/W4300026339","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W2367535589","https://openalex.org/W2348298710","https://openalex.org/W1976521968","https://openalex.org/W2137880375","https://openalex.org/W2351903987","https://openalex.org/W2136336099","https://openalex.org/W2550293690","https://openalex.org/W1529195008","https://openalex.org/W2357224165","https://openalex.org/W2139574475"],"abstract_inverted_index":{"For":[0],"real":[1],"symmetric":[2],"matrices":[3],"that":[4,92],"are":[5,141],"accessible":[6],"only":[7],"through":[8],"matrix":[9,59,81],"vector":[10],"products,":[11],"we":[12],"present":[13],"Monte":[14,33],"Carlo":[15,34],"estimators":[16,35,97],"for":[17,25,69,144],"computing":[18],"the":[19,80,93,96,100,104,132,142],"diagonal":[20,101],"elements.":[21],"Our":[22,72],"probabilistic":[23],"bounds":[24,73],"normwise":[26],"absolute":[27],"and":[28,42,44,48,90,112,148],"relative":[29],"errors":[30],"apply":[31],"to":[32,49,107,154],"based":[36],"on":[37,79,125],"random":[38],"Rademacher,":[39,41],"sparse":[40,137],"normalized":[43],"unnormalized":[45],"Gaussian":[46],"vectors":[47,50],"with":[51,99],"bounded":[52],"fourth":[53],"moments.":[54],"The":[55],"novel":[56],"use":[57,133],"of":[58,95,103,136,159],"concentration":[60],"inequalities":[61],"in":[62,116,134],"our":[63],"proofs":[64],"represents":[65],"a":[66,157],"systematic":[67],"model":[68],"future":[70],"analyses.":[71],"mostly":[74],"do":[75,122],"not":[76],"depend":[77],"explicitly":[78],"dimension,":[82],"target":[83],"different":[84],"error":[85],"measures":[86,115],"than":[87],"existing":[88],"work,":[89],"imply":[91],"accuracy":[94,160],"increases":[98],"dominance":[102],"matrix.":[105],"Applications":[106],"derivative-based":[108],"global":[109],"sensitivity":[110],"metrics":[111],"node":[113],"centrality":[114],"network":[117],"science":[118],"corroborate":[119],"this,":[120],"as":[121],"numerical":[123],"experiments":[124],"synthetic":[126],"test":[127],"matrices.":[128],"We":[129],"recommend":[130],"against":[131],"practice":[135],"Rademacher":[138],"vectors,":[139],"which":[140],"basis":[143],"many":[145],"randomized":[146],"sketching":[147],"sampling":[149,164],"algorithms,":[150],"because":[151],"they":[152],"tend":[153],"deliver":[155],"barely":[156],"digit":[158],"even":[161],"under":[162],"large":[163],"amounts.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}