{"id":"https://openalex.org/W2190254461","doi":"https://doi.org/10.1137/15m1052007","title":"Bounds for the Distance to the Nearest Correlation Matrix","display_name":"Bounds for the Distance to the Nearest Correlation Matrix","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2190254461","doi":"https://doi.org/10.1137/15m1052007","mag":"2190254461"},"language":"en","primary_location":{"id":"doi:10.1137/15m1052007","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1052007","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1052007","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1052007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069339254","display_name":"Nicholas J. Higham","orcid":"https://orcid.org/0000-0001-5956-4976"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nicholas J. Higham","raw_affiliation_strings":["Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064997030","display_name":"Nata\u0161a Strabi\u0107","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nata\u0161a Strabi\u0107","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069339254"],"corresponding_institution_ids":["https://openalex.org/I4210131439"],"apc_list":null,"apc_paid":{"value":2258,"currency":"EUR","value_usd":2435},"fwci":0.7188,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73260997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"37","issue":"3","first_page":"1088","last_page":"1102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7667043209075928},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4720802307128906},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.4439125657081604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3739316463470459},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3585236668586731},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16034546494483948}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7667043209075928},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4720802307128906},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.4439125657081604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3739316463470459},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3585236668586731},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16034546494483948},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1052007","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1052007","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1052007","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9d40a91d-9a24-4be4-9b47-a6fd46d79052","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/9d40a91d-9a24-4be4-9b47-a6fd46d79052","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Higham, N & Strabic, N 2016, 'Bounds for the distance to the nearest correlation matrix', SIAM Journal on Matrix Analysis and Applications, vol. 37, no. 3, pp. 1188-1102. https://doi.org/10.1137/15M1052007","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2420","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:pure.atira.dk:publications/9d40a91d-9a24-4be4-9b47-a6fd46d79052","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/bounds-for-the-distance-to-the-nearest-correlation-matrix(9d40a91d-9a24-4be4-9b47-a6fd46d79052).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Higham, N & Strabic, N 2016, 'Bounds for the distance to the nearest correlation matrix', SIAM Journal on Matrix Analysis and Applications, vol. 37, no. 3, pp. 1188-1102. https://doi.org/10.1137/15M1052007","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1137/15m1052007","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1052007","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1052007","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4408778592","display_name":"Network: Numerical Algorithms and High Performance Computing.","funder_award_id":"EP/I03112X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5407770375","display_name":null,"funder_award_id":"267526","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G6297168181","display_name":null,"funder_award_id":"EP/I01912X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6934807324","display_name":"MAPLE: MAthematics PLatform Engagement activity","funder_award_id":"EP/I01912X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7674845474","display_name":null,"funder_award_id":"EP/I03112X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2190254461.pdf","grobid_xml":"https://content.openalex.org/works/W2190254461.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1599048743","https://openalex.org/W1859634276","https://openalex.org/W1955055489","https://openalex.org/W1982165727","https://openalex.org/W1982248339","https://openalex.org/W2002070806","https://openalex.org/W2012275962","https://openalex.org/W2016070917","https://openalex.org/W2025986317","https://openalex.org/W2032711963","https://openalex.org/W2035754171","https://openalex.org/W2037430361","https://openalex.org/W2037605414","https://openalex.org/W2050958540","https://openalex.org/W2053627399","https://openalex.org/W2061281381","https://openalex.org/W2067910989","https://openalex.org/W2072175279","https://openalex.org/W2072863821","https://openalex.org/W2074070708","https://openalex.org/W2079963825","https://openalex.org/W2091560152","https://openalex.org/W2104481149","https://openalex.org/W2130697848","https://openalex.org/W2154815749","https://openalex.org/W2499991388","https://openalex.org/W3122058357","https://openalex.org/W3125359024","https://openalex.org/W3173138228"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W4230347692","https://openalex.org/W2351859806","https://openalex.org/W2127487771","https://openalex.org/W4234080744","https://openalex.org/W3035458135","https://openalex.org/W4239376463"],"abstract_inverted_index":{"In":[0],"a":[1,13,19,30,65,74,81,119,128,162,167,202,223],"wide":[2],"range":[3],"of":[4,32,52,77,83,130,146,149,192,199],"practical":[5,137],"problems":[6],"correlation":[7,47,96,195,208,229],"matrices":[8,131],"are":[9,22,51,87,112,142,175],"formed":[10],"in":[11],"such":[12,225],"way":[14,187],"that,":[15],"while":[16],"symmetry":[17],"and":[18,61,135,182,212],"unit":[20,100],"diagonal":[21,101],"ensured,":[23],"they":[24,183],"may":[25],"lack":[26],"semidefiniteness.":[27],"We":[28,124],"derive":[29],"variety":[31],"new":[33],"upper":[34,156],"bounds":[35,50,111,141,174,200],"for":[36,80,105,127,190],"the":[37,45,59,94,109,116,133,139,150,154,193,227],"distance":[38,117],"from":[39,70,132,136],"an":[40,185,206],"arbitrary":[41],"symmetric":[42],"matrix":[43,82,97,209],"to":[44,91,114,188,204,213,216,221],"nearest":[46,95,228],"matrix.":[48,196,230],"The":[49,171],"two":[53],"main":[54],"classes:":[55],"those":[56,62],"based":[57,63],"on":[58,64],"eigensystem":[60,110],"modified":[66,172],"Cholesky":[67,173],"factorization.":[68],"Bounds":[69],"both":[71],"classes":[72,198],"have":[73],"computational":[75],"cost":[76],"$O(n^3)$":[78],"flops":[79],"order":[84,145],"$n$":[85],"but":[86,178],"much":[88],"less":[89,176,180],"expensive":[90],"evaluate":[92],"than":[93,161,166],"itself.":[98],"For":[99],"$A$":[102],"with":[103],"$|a_{ij}|\\leq1$":[104],"all":[106],"$i\\neq":[107],"j$":[108],"shown":[113],"overestimate":[115],"by":[118],"factor":[120,163],"at":[121],"most":[122],"$1+n\\sqrt{n}$.":[123],"show":[125],"that":[126],"collection":[129],"literature":[134],"applications":[138],"eigensystem-based":[140],"often":[143],"good":[144],"magnitude":[147],"estimates":[148],"actual":[151],"distance;":[152],"indeed":[153],"best":[155],"bound":[157],"is":[158],"never":[159],"more":[160],"5":[164],"larger":[165],"related":[168],"lower":[169],"bound.":[170],"sharp":[177],"also":[179],"expensive,":[181],"provide":[184],"efficient":[186],"test":[189],"definiteness":[191],"putative":[194],"Both":[197],"enable":[201],"user":[203],"identify":[205],"invalid":[207],"relatively":[210],"cheaply":[211],"decide":[214],"whether":[215],"revisit":[217],"its":[218],"construction":[219],"or":[220],"compute":[222],"replacement,":[224],"as":[226]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}