{"id":"https://openalex.org/W1980271325","doi":"https://doi.org/10.1137/s0895479899350976","title":"Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches","display_name":"Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1980271325","doi":"https://doi.org/10.1137/s0895479899350976","mag":"1980271325"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899350976","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899350976","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/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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001684645","display_name":"Hyun\u2010Min Kim","orcid":"https://orcid.org/0000-0003-4610-3606"},"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":false,"raw_author_name":"Hyun-Min Kim","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester, M13 9PL, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Manchester, M13 9PL, England","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069339254"],"corresponding_institution_ids":["https://openalex.org/I4210131439"],"apc_list":null,"apc_paid":null,"fwci":2.2892,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.87162162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"23","issue":"2","first_page":"303","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.7997407913208008},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6992241144180298},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.646371066570282},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6172059774398804},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.6164053678512573},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6041366457939148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5583467483520508},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.5056815147399902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11746478080749512},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06423044204711914},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0554356575012207}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7997407913208008},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6992241144180298},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.646371066570282},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6172059774398804},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.6164053678512573},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6041366457939148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5583467483520508},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.5056815147399902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11746478080749512},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06423044204711914},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0554356575012207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0895479899350976","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899350976","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"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9a362bd7-da05-421f-95a0-c659a2318862","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/9a362bd7-da05-421f-95a0-c659a2318862","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 & Kim, H M 2002, 'Solving a quadratic matrix equation by Newton's method with exact line searches', SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 2, pp. 303-316. https://doi.org/10.1137/S0895479899350976","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:319","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:hdl:10068/647482","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/647482","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W197984925","https://openalex.org/W358598360","https://openalex.org/W1488435683","https://openalex.org/W1557025970","https://openalex.org/W1573717114","https://openalex.org/W1575866755","https://openalex.org/W1600349401","https://openalex.org/W1965502743","https://openalex.org/W1977243335","https://openalex.org/W1981334692","https://openalex.org/W1987035720","https://openalex.org/W1991261345","https://openalex.org/W2000630868","https://openalex.org/W2007337094","https://openalex.org/W2022405282","https://openalex.org/W2036056640","https://openalex.org/W2040608867","https://openalex.org/W2040769287","https://openalex.org/W2041197714","https://openalex.org/W2044431299","https://openalex.org/W2045973172","https://openalex.org/W2046758878","https://openalex.org/W2054557544","https://openalex.org/W2054689585","https://openalex.org/W2068484625","https://openalex.org/W2075194837","https://openalex.org/W2077658674","https://openalex.org/W2083796083","https://openalex.org/W2086846400","https://openalex.org/W2094210158","https://openalex.org/W2097156328","https://openalex.org/W2123783510","https://openalex.org/W2133936817","https://openalex.org/W2171435898","https://openalex.org/W2171562370","https://openalex.org/W2798909945","https://openalex.org/W4212997115","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1546266651","https://openalex.org/W4289793162","https://openalex.org/W2108283631","https://openalex.org/W2107915509","https://openalex.org/W1967942590","https://openalex.org/W2035394906","https://openalex.org/W4376455749","https://openalex.org/W2538271650","https://openalex.org/W2167137033","https://openalex.org/W2048294433"],"abstract_inverted_index":{"We":[0,52],"show":[1,62],"how":[2,63],"to":[3,64],"incorporate":[4],"exact":[5],"line":[6,33],"searches":[7,34],"into":[8],"Newton's":[9,45],"method":[10,46],"for":[11,58],"solving":[12],"the":[13,40,59,66],"quadratic":[14],"matrix":[15],"equation":[16],"AX2":[17],"+":[18,20],"BX":[19],"C":[21,28],"=":[22],"0,":[23],"where":[24],"A,":[25],"B":[26],"and":[27,38,49,61],"are":[29,35],"square":[30],"matrices.":[31],"The":[32],"relatively":[36],"inexpensive":[37],"improve":[39],"global":[41],"convergence":[42],"properties":[43],"of":[44,69],"in":[47,50],"theory":[48],"practice.":[51],"also":[53],"derive":[54],"a":[55],"condition":[56],"number":[57],"problem":[60],"compute":[65],"backward":[67],"error":[68],"an":[70],"approximate":[71],"solution.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}