{"id":"https://openalex.org/W2050283228","doi":"https://doi.org/10.1090/s0025-5718-98-00978-8","title":"Factorizing complex symmetric matrices with positive definite real and imaginary parts","display_name":"Factorizing complex symmetric matrices with positive definite real and imaginary parts","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2050283228","doi":"https://doi.org/10.1090/s0025-5718-98-00978-8","mag":"2050283228"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00978-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00978-8","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00978-8/S0025-5718-98-00978-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00978-8/S0025-5718-98-00978-8.pdf","any_repository_has_fulltext":false},"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/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Nicholas Higham","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester, M13 9PL, England","Department of Mathematics, University of Manchester Manchester, M13 9PL, England#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Manchester, M13 9PL, England","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Mathematics, University of Manchester Manchester, M13 9PL, England#TAB#","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069339254"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":1.0173,"has_fulltext":true,"cited_by_count":43,"citation_normalized_percentile":{"value":0.76439381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"67","issue":"224","first_page":"1591","last_page":"1599"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5734017491340637},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4369371235370636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43677830696105957},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4217088222503662},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3537558317184448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1277046501636505}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5734017491340637},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4369371235370636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43677830696105957},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4217088222503662},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3537558317184448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1277046501636505}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-98-00978-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00978-8","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00978-8/S0025-5718-98-00978-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/3ad3a353-38c3-4e9d-a08d-daff9b997c5a","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/3ad3a353-38c3-4e9d-a08d-daff9b997c5a","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, N J 1998, 'Factorizing complex symmetric matrices with positive definite real and imaginary parts', Mathematics of Computation, vol. 67, no. 224, pp. 1591-1599.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:337","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":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3654","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1998-67-224/S0025-5718-98-00978-8/S0025-5718-98-00978-8.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00978-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00978-8","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00978-8/S0025-5718-98-00978-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2050283228.pdf","grobid_xml":"https://content.openalex.org/works/W2050283228.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W133977063","https://openalex.org/W1480928214","https://openalex.org/W1968185752","https://openalex.org/W1985982749","https://openalex.org/W1992155051","https://openalex.org/W2000250112","https://openalex.org/W2010237532","https://openalex.org/W2011537842","https://openalex.org/W2020804487","https://openalex.org/W2021982403","https://openalex.org/W2031392034","https://openalex.org/W2038648365","https://openalex.org/W2039827140","https://openalex.org/W2044180130","https://openalex.org/W2056283416","https://openalex.org/W2068633006","https://openalex.org/W2069691448","https://openalex.org/W2075998338","https://openalex.org/W2167496141","https://openalex.org/W3022909171","https://openalex.org/W4230129384","https://openalex.org/W4239941700"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Complex":[0],"symmetric":[1],"matrices":[2,103],"whose":[3],"real":[4],"and":[5,91,96,129,167],"imaginary":[6],"parts":[7],"are":[8,11,127],"positive":[9],"definite":[10],"shown":[12,99],"to":[13,27,37,41],"have":[14],"a":[15],"growth":[16,132],"factor":[17,133],"bounded":[18],"by":[19],"2":[20,136],"for":[21,32,101],"LU":[22,44],"factorization.":[23,45],"This":[24],"result":[25],"adds":[26],"the":[28,86,130,153,157,162],"classes":[29],"of":[30,89,135],"matrix":[31],"which":[33],"it":[34,97],"is":[35,93,98],"known":[36],"be":[38,146],"safe":[39],"not":[40],"pivot":[42],"in":[43,165],"Block":[46],"<inline-formula":[47,105],"content-type=\"math/mathml\">":[48,106],"<mml:math":[49,107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50,108],"alttext=\"normal":[51],"upper":[52,55,58,62],"L":[53,59],"normal":[54,57,61],"D":[56],"Superscript":[60],"T\">":[63],"<mml:semantics>":[64,112],"<mml:mrow":[65],"class=\"MJX-TeXAtom-ORD\">":[66],"<mml:mi":[67,69,72,74],"mathvariant=\"normal\">L</mml:mi>":[68,73],"mathvariant=\"normal\">D</mml:mi>":[70],"<mml:msup>":[71],"mathvariant=\"normal\">T</mml:mi>":[75],"</mml:msup>":[76],"</mml:mrow>":[77,119],"<mml:annotation":[78,120],"encoding=\"application/x-tex\">\\mathrm":[79],"{LDL^T}</mml:annotation>":[80],"</mml:semantics>":[81,123],"</mml:math>":[82,124],"</inline-formula>":[83,125],"factorization":[84],"with":[85],"pivoting":[87,154],"strategy":[88,155],"Bunch":[90],"Kaufman":[92],"also":[94],"considered,":[95],"that":[100,139,141],"such":[102],"only":[104],"alttext=\"1":[109],"times":[110],"1\">":[111],"<mml:mrow>":[113],"<mml:mn>1</mml:mn>":[114,118],"<mml:mo>":[115],"\u00d7":[116],"</mml:mo>":[117],"encoding=\"application/x-tex\">1\\times":[121],"1</mml:annotation>":[122],"pivots":[126],"used":[128],"same":[131],"bound":[134],"holds,":[137],"but":[138],"interchanges":[140],"destroy":[142],"band":[143],"structure":[144],"may":[145],"made.":[147],"The":[148],"latter":[149],"results":[150],"hold":[151],"whether":[152],"uses":[156],"usual":[158],"absolute":[159],"value":[160],"or":[161],"modification":[163],"employed":[164],"LINPACK":[166],"LAPACK.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":10}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
