{"id":"https://openalex.org/W2152097197","doi":"https://doi.org/10.1109/acc.2009.5159824","title":"Gradient-based iterative solutions for general matrix equations","display_name":"Gradient-based iterative solutions for general matrix equations","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2152097197","doi":"https://doi.org/10.1109/acc.2009.5159824","mag":"2152097197"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2009.5159824","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5159824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-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/A5100365449","display_name":"Xie Li","orcid":"https://orcid.org/0000-0002-7497-8402"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Xie","raw_affiliation_strings":["School of Communication and Control Engineering, Jiangnan University, Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Control Engineering, Jiangnan University, Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051959906","display_name":"Huizhong Yang","orcid":"https://orcid.org/0000-0001-9038-4797"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huizhong Yang","raw_affiliation_strings":["School of Communication and Control Engineering, Jiangnan University, Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Control Engineering, Jiangnan University, Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015758351","display_name":"Jie Ding","orcid":"https://orcid.org/0000-0002-9910-6280"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Ding","raw_affiliation_strings":["School of Communication and Control Engineering, Jiangnan University, Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Control Engineering, Jiangnan University, Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100637638","display_name":"Feng Ding","orcid":"https://orcid.org/0000-0002-2721-2025"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Ding","raw_affiliation_strings":["School of Communication and Control Engineering, Jiangnan University, Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Control Engineering, Jiangnan University, Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7701,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78987683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"500","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11236","display_name":"Control Systems and Identification","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.994700014591217,"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/iterative-method","display_name":"Iterative method","score":0.7790489196777344},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6657435894012451},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5937976837158203},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5902833938598633},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.5381826162338257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5043171644210815},{"id":"https://openalex.org/keywords/matrix-free-methods","display_name":"Matrix-free methods","score":0.47591525316238403},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4692551791667938},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.457705020904541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45754122734069824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4460330605506897},{"id":"https://openalex.org/keywords/convergent-matrix","display_name":"Convergent matrix","score":0.4158734083175659},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.4103314280509949},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3188777565956116},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.3188096284866333},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.26062461733818054},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07005700469017029}],"concepts":[{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.7790489196777344},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6657435894012451},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5937976837158203},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5902833938598633},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.5381826162338257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5043171644210815},{"id":"https://openalex.org/C54219892","wikidata":"https://www.wikidata.org/wiki/Q4080929","display_name":"Matrix-free methods","level":4,"score":0.47591525316238403},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4692551791667938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.457705020904541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45754122734069824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4460330605506897},{"id":"https://openalex.org/C9848182","wikidata":"https://www.wikidata.org/wiki/Q5166397","display_name":"Convergent matrix","level":5,"score":0.4158734083175659},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.4103314280509949},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3188777565956116},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.3188096284866333},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.26062461733818054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07005700469017029},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2009.5159824","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5159824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W150065341","https://openalex.org/W1970280663","https://openalex.org/W1972652206","https://openalex.org/W1981745143","https://openalex.org/W1986910338","https://openalex.org/W2019606797","https://openalex.org/W2023892559","https://openalex.org/W2033732506","https://openalex.org/W2033966841","https://openalex.org/W2047751572","https://openalex.org/W2049871086","https://openalex.org/W2054463619","https://openalex.org/W2056615320","https://openalex.org/W2066021453","https://openalex.org/W2069511885","https://openalex.org/W2072281876","https://openalex.org/W2093958427","https://openalex.org/W2113304978","https://openalex.org/W2136291495","https://openalex.org/W2138844572","https://openalex.org/W2150677167","https://openalex.org/W2155848675","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W4380271776","https://openalex.org/W2015081464","https://openalex.org/W2366222664","https://openalex.org/W2050716149","https://openalex.org/W2374901252","https://openalex.org/W2161209494","https://openalex.org/W2005314356","https://openalex.org/W2060899753","https://openalex.org/W2306757564","https://openalex.org/W2341430035"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"solutions":[5,32,39],"of":[6,48],"general":[7],"matrix":[8],"equations":[9],"by":[10,20],"using":[11],"the":[12,22,30,37,49],"iterative":[13,18,31],"method":[14],"and":[15,44],"present":[16],"gradient-based":[17],"algorithms":[19],"applying":[21],"hierarchical":[23],"identification":[24],"principle.":[25],"Convergence":[26],"analysis":[27],"indicates":[28],"that":[29],"always":[33],"converge":[34],"fast":[35],"to":[36],"exact":[38],"for":[40],"any":[41],"initial":[42],"values":[43],"small":[45],"condition":[46],"numbers":[47],"associated":[50],"matrices.":[51],"Several":[52],"numerical":[53],"examples":[54],"are":[55],"included.":[56]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
