{"id":"https://openalex.org/W1979403862","doi":"https://doi.org/10.1137/s0895479899345571","title":"On an Iteration Method for Solving a Class of Nonlinear Matrix Equations","display_name":"On an Iteration Method for Solving a Class of Nonlinear Matrix Equations","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1979403862","doi":"https://doi.org/10.1137/s0895479899345571","mag":"1979403862"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899345571","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899345571","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/A5069850068","display_name":"Salah M. El\u2010Sayed","orcid":"https://orcid.org/0000-0001-9885-313X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Salah M. El-Sayed","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087614381","display_name":"Andr\u00e9 C. M. Ran","orcid":"https://orcid.org/0000-0001-9868-8605"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 C. M. Ran","raw_affiliation_strings":["Vrije Universiteit Amsterdam ,"],"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam ,","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069850068"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.299,"has_fulltext":false,"cited_by_count":117,"citation_normalized_percentile":{"value":0.97254287,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"23","issue":"3","first_page":"632","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.995199978351593,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9930999875068665,"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":0.9062229990959167},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.890335202217102},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6314575672149658},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4945211112499237},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48249340057373047},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44388383626937866},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4367055594921112},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.4214727580547333},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.39290791749954224},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.353168249130249},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3257729411125183},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07176342606544495}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9062229990959167},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.890335202217102},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6314575672149658},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4945211112499237},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48249340057373047},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44388383626937866},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4367055594921112},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.4214727580547333},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.39290791749954224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.353168249130249},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3257729411125183},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07176342606544495},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895479899345571","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899345571","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:research.vu.nl:openaire_cris_publications/cb961d11-06ab-4ba6-96ec-f2b679cad5b1","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/cb961d11-06ab-4ba6-96ec-f2b679cad5b1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"El-Sayed, S M & Ran, A C M 2002, 'On an iteration method for solving a class of nonlinear matrix equations', SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 3, pp. 632-645 (electronic). https://doi.org/10.1137/S0895479899345571","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:vu:oai:research.vu.nl:publications/cb961d11-06ab-4ba6-96ec-f2b679cad5b1","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/cb961d11-06ab-4ba6-96ec-f2b679cad5b1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 23(3), 632 - 645 (electronic). Society for Industrial and Applied Mathematics Publications","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1510461155","https://openalex.org/W1600349401","https://openalex.org/W1965452869","https://openalex.org/W1975886185","https://openalex.org/W1976335834","https://openalex.org/W2002156977","https://openalex.org/W2007322084","https://openalex.org/W2017401723","https://openalex.org/W2020833279","https://openalex.org/W2029822378","https://openalex.org/W2051352619","https://openalex.org/W2128978199","https://openalex.org/W2145933873","https://openalex.org/W2463195734","https://openalex.org/W2798707604","https://openalex.org/W4255333822","https://openalex.org/W4388319978"],"related_works":["https://openalex.org/W1502458949","https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W2323830966","https://openalex.org/W4380682190","https://openalex.org/W2362838148","https://openalex.org/W2102386043","https://openalex.org/W1605098306","https://openalex.org/W4297909333"],"abstract_inverted_index":{"This":[0],"paper":[1],"treats":[2],"a":[3,41,57],"set":[4],"of":[5,66,88],"equationsof":[6],"the":[7,64,89],"form":[8],"$X+A^{\\star}{\\cal":[9],"F}(X)A":[10],"=Q$,":[11],"where":[12],"${\\cal":[13],"F}$":[14],"maps":[15],"positive":[16,21,42,58],"definite":[17,22,27,43,59],"matrices":[18,23],"either":[19],"into":[20,25],"or":[24],"negative":[26],"matrices,":[28],"and":[29,38,73],"satisfies":[30],"some":[31,50,74],"monotonicity":[32],"property.":[33],"Here":[34],"A":[35],"is":[36,40,46,68],"arbitrary":[37],"Q":[39],"matrix.":[44],"It":[45],"shown":[47],"that":[48],"under":[49,70],"conditions":[51],"an":[52],"iteration":[53],"method":[54],"converges":[55],"to":[56],"solution.":[60],"An":[61],"estimate":[62],"for":[63],"rate":[65],"convergence":[67],"given":[69],"additional":[71],"conditions,":[72],"numerical":[75],"results":[76],"are":[77,81],"given.":[78],"Special":[79],"cases":[80,87],"considered,":[82],"which":[83],"cover":[84],"also":[85],"particular":[86],"discrete":[90],"algebraic":[91],"Riccati":[92],"equation.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
