{"id":"https://openalex.org/W3043589213","doi":"https://doi.org/10.1137/20m1338149","title":"Random Matrices Generating Large Growth in LU Factorization with Pivoting","display_name":"Random Matrices Generating Large Growth in LU Factorization with Pivoting","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3043589213","doi":"https://doi.org/10.1137/20m1338149","mag":"3043589213"},"language":"en","primary_location":{"id":"doi:10.1137/20m1338149","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1338149","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":"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://doi.org/10.1137/20m1338149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058486589","display_name":"Desmond J. Higham","orcid":"https://orcid.org/0000-0002-6635-3461"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Desmond J. Higham","raw_affiliation_strings":["\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069339254","display_name":"Nicholas J. Higham","orcid":"https://orcid.org/0000-0001-5956-4976"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nicholas J. Higham","raw_affiliation_strings":["\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK"],"raw_orcid":"https://orcid.org/0000-0001-5956-4976","affiliations":[{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070702896","display_name":"Srikara Pranesh","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Srikara Pranesh","raw_affiliation_strings":["\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"\\dagger School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070702896"],"corresponding_institution_ids":["https://openalex.org/I28407311","https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.9588,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83772999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"1","first_page":"185","last_page":"201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7858189940452576},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.557796835899353},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5559064149856567},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.544590175151825},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5231165289878845},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5152221322059631},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.46568337082862854},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4150004982948303},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.4120180904865265},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18668889999389648},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14576846361160278},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13171935081481934}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7858189940452576},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.557796835899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5559064149856567},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.544590175151825},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5231165289878845},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5152221322059631},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.46568337082862854},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4150004982948303},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.4120180904865265},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18668889999389648},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14576846361160278},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13171935081481934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1338149","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1338149","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":"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/63e72b70-0200-42b6-a27e-04f2c80106ae","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/63e72b70-0200-42b6-a27e-04f2c80106ae","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Higham, D J, Higham, N & Pranesh, S 2020, 'Random Matrices Generating Large Growth in Lu Factorization with Pivoting', SIAM Journal on Matrix Analysis and Applications.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2764","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.ed.ac.uk:publications/691f5a2b-319b-4013-91c9-53b675243682","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/691f5a2b-319b-4013-91c9-53b675243682","pdf_url":"http://hdl.handle.net/20.500.11820/691f5a2b-319b-4013-91c9-53b675243682","source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1137/20m1338149","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1338149","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":"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/G1322834978","display_name":"Inference, COmputation and Numerics for Insights into Cities (ICONIC)","funder_award_id":"EP/P020720/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1935751110","display_name":null,"funder_award_id":"EP/P020720/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W106789774","https://openalex.org/W658559791","https://openalex.org/W1488226989","https://openalex.org/W1976662650","https://openalex.org/W1999202513","https://openalex.org/W2009774414","https://openalex.org/W2013737143","https://openalex.org/W2025614228","https://openalex.org/W2025626352","https://openalex.org/W2037476261","https://openalex.org/W2041364558","https://openalex.org/W2053489736","https://openalex.org/W2076724857","https://openalex.org/W2078126355","https://openalex.org/W2086258274","https://openalex.org/W2086351984","https://openalex.org/W2089817321","https://openalex.org/W2099641086","https://openalex.org/W2104849640","https://openalex.org/W2115780241","https://openalex.org/W2132657058","https://openalex.org/W2149733240","https://openalex.org/W2165917639","https://openalex.org/W2599973081","https://openalex.org/W2752879223","https://openalex.org/W2808102735","https://openalex.org/W2895305554","https://openalex.org/W2907265372","https://openalex.org/W2910374893","https://openalex.org/W2937715180","https://openalex.org/W2964303560","https://openalex.org/W3022909171","https://openalex.org/W3103446221","https://openalex.org/W3108141724"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W2010100052","https://openalex.org/W1990844505","https://openalex.org/W1607100495","https://openalex.org/W4378770618","https://openalex.org/W4386721910","https://openalex.org/W2148568324","https://openalex.org/W2274293306","https://openalex.org/W2140805692"],"abstract_inverted_index":{"We":[0,142,183],"identify":[1],"a":[2,20,88,129,188],"class":[3],"of":[4,17,24,37,78,125,128,201],"random,":[5],"dense,":[6],"$n\\times":[7],"n$":[8],"matrices":[9,39,54,62,82,172],"for":[10,31,49,113,139,150,170,198],"which":[11,99],"LU":[12,232],"factorization":[13],"with":[14,55,87,173],"any":[15,126,199],"form":[16,200],"pivoting":[18,152,202],"produces":[19],"growth":[21,46,116,155,168,197,206,227],"factor":[22],"typically":[23],"size":[25],"at":[26],"least":[27],"$n/(4":[28],"\\log":[29],"n)$":[30],"large":[32,45,115,140,196,205,226],"$n$.":[33,141],"The":[34,61],"condition":[35],"number":[36],"the":[38,50,67,76,84,114,118,121,144,153,160,167,176],"can":[40,63,217],"be":[41,64,136],"arbitrarily":[42],"chosen,":[43],"and":[44,71,103,147,163],"also":[47,203],"happens":[48],"transpose.":[51],"Previously,":[52],"no":[53],"all":[56],"these":[57],"properties":[58],"were":[59],"known.":[60],"generated":[65],"by":[66],"MATLAB":[68],"function":[69],"gallery('randsvd',...),":[70],"they":[72],"are":[73],"formed":[74],"as":[75],"product":[77],"two":[79],"random":[80,171],"orthogonal":[81,132,193],"from":[83,97,175],"Haar":[85,130],"distribution":[86],"diagonal":[89,94],"matrix":[90,133,194],"having":[91],"only":[92],"one":[93],"entry":[95],"different":[96],"1,":[98],"lies":[100],"between":[101],"0":[102],"1":[104],"(the":[105],"\u201cone":[106],"small":[107,138],"singular":[108],"value\u201d":[109],"case).":[110],"Our":[111],"explanation":[112],"uses":[117],"fact":[119],"that":[120,149,187,213],"maximum":[122],"absolute":[123],"value":[124],"element":[127],"distributed":[131],"tends":[134],"to":[135,191,221],"relatively":[137],"verify":[143],"behavior":[145],"numerically":[146],"find":[148],"partial":[151],"actual":[154],"is":[156],"significantly":[157],"larger":[158,165],"than":[159,166],"lower":[161],"bound":[162],"much":[164],"observed":[169],"elements":[174],"uniform":[177],"[0,1]":[178],"or":[179],"standard":[180,236],"normal":[181],"distributions.":[182],"show":[184],"more":[185],"generally":[186],"rank-1":[189],"perturbation":[190],"an":[192],"producing":[195],"generates":[204],"under":[207],"reasonable":[208],"assumptions.":[209],"Finally,":[210],"we":[211],"demonstrate":[212],"GMRES-based":[214],"iterative":[215,237],"refinement":[216,238],"provide":[218],"stable":[219],"solutions":[220],"$Ax":[222],"=":[223],"b$":[224],"when":[225,235],"occurs":[228],"in":[229],"low":[230],"precision":[231],"factors,":[233],"even":[234],"cannot.":[239]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}