{"id":"https://openalex.org/W2138244240","doi":"https://doi.org/10.1109/tcsi.2008.2007065","title":"From Zhang Neural Network to Newton Iteration for Matrix Inversion","display_name":"From Zhang Neural Network to Newton Iteration for Matrix Inversion","publication_year":2008,"publication_date":"2008-11-12","ids":{"openalex":"https://openalex.org/W2138244240","doi":"https://doi.org/10.1109/tcsi.2008.2007065","mag":"2138244240"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2008.2007065","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.2007065","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/A5053064477","display_name":"Yunong Zhang","orcid":"https://orcid.org/0000-0002-2228-0395"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunong Zhang","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100922585","display_name":"Weimu Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weimu Ma","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038278967","display_name":"Binghuang Cai","orcid":"https://orcid.org/0000-0002-0348-0690"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binghuang Cai","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Dept..of Electron. & Commun. Eng., Sun Yat-Sen Univ., Guangzhou, , China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":9.9235,"has_fulltext":false,"cited_by_count":192,"citation_normalized_percentile":{"value":0.97898141,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"56","issue":"7","first_page":"1405","last_page":"1415"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9936000108718872,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9901999831199646,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.7135674953460693},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6088405251502991},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5662532448768616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5312212705612183},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5066357254981995},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4935818910598755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45010870695114136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44607147574424744},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42440593242645264},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23478493094444275},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07908010482788086},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07738879323005676}],"concepts":[{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.7135674953460693},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6088405251502991},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5662532448768616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5312212705612183},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5066357254981995},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4935818910598755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45010870695114136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44607147574424744},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42440593242645264},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23478493094444275},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07908010482788086},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07738879323005676},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcsi.2008.2007065","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.2007065","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/15241","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/15241","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W203018206","https://openalex.org/W282155574","https://openalex.org/W391578156","https://openalex.org/W1484735710","https://openalex.org/W1538983967","https://openalex.org/W1545318875","https://openalex.org/W1578671836","https://openalex.org/W1802825888","https://openalex.org/W1996705509","https://openalex.org/W1997270899","https://openalex.org/W2006860831","https://openalex.org/W2014530379","https://openalex.org/W2028190538","https://openalex.org/W2037181055","https://openalex.org/W2051385641","https://openalex.org/W2053498134","https://openalex.org/W2077847045","https://openalex.org/W2085165200","https://openalex.org/W2091101062","https://openalex.org/W2099636542","https://openalex.org/W2100128021","https://openalex.org/W2105363862","https://openalex.org/W2115098233","https://openalex.org/W2124619121","https://openalex.org/W2124776405","https://openalex.org/W2129119560","https://openalex.org/W2130317597","https://openalex.org/W2131241181","https://openalex.org/W2132423763","https://openalex.org/W2133253631","https://openalex.org/W2133702739","https://openalex.org/W2138398260","https://openalex.org/W2146341299","https://openalex.org/W2158831443","https://openalex.org/W2163760546","https://openalex.org/W2165552175","https://openalex.org/W2489292218","https://openalex.org/W2610857016","https://openalex.org/W2798909945","https://openalex.org/W4253756272"],"related_works":["https://openalex.org/W2902723393","https://openalex.org/W2386387936","https://openalex.org/W2392110728","https://openalex.org/W2069549023","https://openalex.org/W2350848567","https://openalex.org/W2386767533","https://openalex.org/W2380313759","https://openalex.org/W2086999410","https://openalex.org/W4288081727","https://openalex.org/W2076870043"],"abstract_inverted_index":{"Different":[0,127],"from":[1],"gradient-based":[2],"neural":[3,10,66],"networks,":[4],"a":[5,30,36,61,82],"special":[6,106],"kind":[7],"of":[8,35,50,64,84,118,129,144,151],"recurrent":[9],"network":[11,67],"(RNN)":[12],"has":[13],"recently":[14],"been":[15],"proposed":[16],"by":[17,81],"Zhang":[18,65],"for":[19,75,91,124,138,157],"online":[20,158],"matrix":[21,92,125,159],"inversion.":[22,126,160],"Such":[23],"an":[24,46,51],"RNN":[25],"is":[26,79],"designed":[27],"based":[28],"on":[29,115],"matrix-valued":[31],"error":[32,38],"function":[33],"instead":[34,49],"scalar-valued":[37],"function.":[39],"In":[40,54],"addition,":[41],"it":[42],"was":[43],"depicted":[44,80],"in":[45],"implicit":[47],"dynamics":[48],"explicit":[52],"dynamics.":[53],"this":[55,109],"paper,":[56],"we":[57,94,111],"develop":[58],"and":[59,71,121,132,141,154],"investigate":[60],"discrete-time":[62,98],"model":[63,100],"(termed":[68],"as":[69,73,104],"such":[70],"abbreviated":[72],"ZNN":[74,99,120,153],"presentation":[76],"convenience),":[77],"which":[78],"system":[83],"difference":[85],"equations.":[86],"Comparing":[87],"with":[88],"Newton":[89,102,122,155],"iteration":[90,103,123,156],"inversion,":[93],"find":[95],"that":[96],"the":[97,149],"incorporates":[101],"its":[105],"case.":[107],"Noticing":[108],"relation,":[110],"perform":[112],"numerical":[113],"comparisons":[114],"different":[116,133],"situations":[117],"using":[119],"kinds":[128],"activation":[130],"functions":[131],"step-size":[134],"values":[135],"are":[136],"examined":[137],"superior":[139],"convergence":[140],"better":[142],"stability":[143],"ZNN.":[145],"Numerical":[146],"examples":[147],"demonstrate":[148],"efficacy":[150],"both":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":15}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}