{"id":"https://openalex.org/W2081938492","doi":"https://doi.org/10.1109/icca.2010.5524148","title":"Convergence analysis of Zhang neural networks solving time-varying linear equations but without using time-derivative information","display_name":"Convergence analysis of Zhang neural networks solving time-varying linear equations but without using time-derivative information","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2081938492","doi":"https://doi.org/10.1109/icca.2010.5524148","mag":"2081938492"},"language":"en","primary_location":{"id":"doi:10.1109/icca.2010.5524148","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2010.5524148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE ICCA 2010","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/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":true,"raw_author_name":"Yunong Zhang","raw_affiliation_strings":["School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013551265","display_name":"Yanyan Shi","orcid":"https://orcid.org/0000-0003-2759-0015"},"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":"Yanyan Shi","raw_affiliation_strings":["School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116479885","display_name":"Yiwen Yang","orcid":"https://orcid.org/0000-0003-2136-6602"},"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":"Yiwen Yang","raw_affiliation_strings":["School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035724004","display_name":"Zhende Ke","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":"Zhende Ke","raw_affiliation_strings":["School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China#TAB#","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053064477"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":2.8904,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91640208,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1215","last_page":"1220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9954000115394592,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9954000115394592,"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/T10320","display_name":"Neural Networks and Applications","score":0.9943000078201294,"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/zh\u00e0ng","display_name":"Zh\u00e0ng","score":0.7735614776611328},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7351180911064148},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6966748237609863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6338315606117249},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.552453875541687},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.535085141658783},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5141392350196838},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4750395119190216},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4618721306324005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4550143778324127},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.42085155844688416},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41272270679473877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31779229640960693},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2614983022212982},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09883540868759155}],"concepts":[{"id":"https://openalex.org/C2777045944","wikidata":"https://www.wikidata.org/wiki/Q12170198","display_name":"Zh\u00e0ng","level":3,"score":0.7735614776611328},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7351180911064148},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6966748237609863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6338315606117249},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.552453875541687},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.535085141658783},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5141392350196838},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4750395119190216},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4618721306324005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4550143778324127},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.42085155844688416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41272270679473877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31779229640960693},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2614983022212982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09883540868759155},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political 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/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca.2010.5524148","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2010.5524148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE ICCA 2010","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":24,"referenced_works":["https://openalex.org/W1484735710","https://openalex.org/W1493190793","https://openalex.org/W1545318875","https://openalex.org/W1974210850","https://openalex.org/W1996705509","https://openalex.org/W1997270899","https://openalex.org/W2014530379","https://openalex.org/W2023757295","https://openalex.org/W2028190538","https://openalex.org/W2053498134","https://openalex.org/W2104689584","https://openalex.org/W2105363862","https://openalex.org/W2111346249","https://openalex.org/W2130317597","https://openalex.org/W2130731760","https://openalex.org/W2133253631","https://openalex.org/W2133702739","https://openalex.org/W2158831443","https://openalex.org/W2163760546","https://openalex.org/W2165552175","https://openalex.org/W4253756272","https://openalex.org/W6632624875","https://openalex.org/W6679499382","https://openalex.org/W6683502422"],"related_works":["https://openalex.org/W2364559953","https://openalex.org/W2375840727","https://openalex.org/W2389678104","https://openalex.org/W2375137083","https://openalex.org/W2380507695","https://openalex.org/W2367687999","https://openalex.org/W2387562377","https://openalex.org/W2384722335","https://openalex.org/W4287812222","https://openalex.org/W3020605251"],"abstract_inverted_index":{"For":[0,47],"online":[1],"solution":[2],"of":[3,10,30,58],"time-varying":[4,86],"linear":[5,87],"equations,":[6],"a":[7],"special":[8],"kind":[9],"recurrent":[11,32],"neural":[12,33,38],"networks":[13,34],"has":[14,23],"recently":[15],"been":[16,24],"proposed":[17],"by":[18],"Zhang":[19,37],"et":[20],"al.":[21],"It":[22],"proved":[25],"that":[26],"global":[27,62],"exponential":[28,63],"convergence":[29],"such":[31],"(or":[35],"termed":[36],"networks,":[39],"ZNN,":[40],"for":[41,82,92],"presentation":[42],"convenience)":[43],"can":[44],"be":[45],"achieved.":[46],"easier":[48],"hardware-realization,":[49],"as":[50,52],"well":[51],"to":[53],"find":[54],"out":[55],"the":[56,65,100],"effect":[57],"time-derivative":[59,70],"terms":[60],"on":[61],"convergence,":[64],"ZNN":[66],"model":[67],"with":[68],"no":[69],"information":[71],"is":[72,90],"investigated,":[73],"analyzed":[74],"and":[75,85,94],"simulated":[76],"in":[77],"this":[78],"paper.":[79],"Theoretical":[80],"analysis":[81],"both":[83],"constant":[84],"equations":[88],"solving":[89],"presented":[91],"comparative":[93],"illustrative":[95],"purposes.":[96],"Computer-simulation":[97],"results":[98],"substantiate":[99],"analysis.":[101]},"counts_by_year":[{"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":2018,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}