{"id":"https://openalex.org/W1981980472","doi":"https://doi.org/10.1109/icnsc.2008.4525331","title":"Common Nature of Learning Exemplified by BP and Hopfield Neural Networks for Solving Online a System of Linear Equations","display_name":"Common Nature of Learning Exemplified by BP and Hopfield Neural Networks for Solving Online a System of Linear Equations","publication_year":2008,"publication_date":"2008-04-01","ids":{"openalex":"https://openalex.org/W1981980472","doi":"https://doi.org/10.1109/icnsc.2008.4525331","mag":"1981980472"},"language":"en","primary_location":{"id":"doi:10.1109/icnsc.2008.4525331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icnsc.2008.4525331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Networking, Sensing and Control","raw_type":"proceedings-article"},"type":"conference-paper","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","Sun Yat-sen University, Guangzhou"],"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":"Sun Yat-sen University, Guangzhou","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100349193","display_name":"Zhan Li","orcid":"https://orcid.org/0000-0002-3928-1642"},"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":"Zhan Li","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China","Sun Yat-sen University, Guangzhou"],"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":"Sun Yat-sen University, Guangzhou","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100451984","display_name":"Ke Chen","orcid":"https://orcid.org/0000-0001-9457-9364"},"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":"Ke Chen","raw_affiliation_strings":["School of Software, Sun Yat-Sen University, Guangzhou, China","School of Software, Sun Yat-Sen University, Guangzhou 510275, China.is03chk@mail2.sysu.edu.cn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Software, Sun Yat-Sen University, Guangzhou 510275, China.is03chk@mail2.sysu.edu.cn","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","Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, China. caibh@mail2.sysu.edu.cn"],"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":"Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, China. caibh@mail2.sysu.edu.cn","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":1.259,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78782635,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":null,"first_page":"832","last_page":"836"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T12564","display_name":"Sensor Technology and Measurement Systems","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T13717","display_name":"Advanced Algorithms and Applications","score":0.9524000287055969,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.7789583206176758},{"id":"https://openalex.org/keywords/hopfield-network","display_name":"Hopfield network","score":0.6865225434303284},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6237560510635376},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.5953241586685181},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.48887771368026733},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.462833434343338},{"id":"https://openalex.org/keywords/types-of-artificial-neural-networks","display_name":"Types of artificial neural networks","score":0.45801061391830444},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4524189829826355},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.43446457386016846},{"id":"https://openalex.org/keywords/simultaneous-equations","display_name":"Simultaneous equations","score":0.41969162225723267},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4178895950317383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40001463890075684},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.388015478849411},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.3357769846916199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3041583299636841},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3032439649105072}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7789583206176758},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.6865225434303284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6237560510635376},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.5953241586685181},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.48887771368026733},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.462833434343338},{"id":"https://openalex.org/C177973122","wikidata":"https://www.wikidata.org/wiki/Q7860946","display_name":"Types of artificial neural networks","level":4,"score":0.45801061391830444},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4524189829826355},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.43446457386016846},{"id":"https://openalex.org/C170036204","wikidata":"https://www.wikidata.org/wiki/Q735660","display_name":"Simultaneous equations","level":3,"score":0.41969162225723267},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4178895950317383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40001463890075684},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.388015478849411},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.3357769846916199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3041583299636841},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3032439649105072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icnsc.2008.4525331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icnsc.2008.4525331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Networking, Sensing and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1484735710","https://openalex.org/W2014530379","https://openalex.org/W2028190538","https://openalex.org/W2053498134","https://openalex.org/W2077633635","https://openalex.org/W2077847045","https://openalex.org/W2105363862","https://openalex.org/W2133702739","https://openalex.org/W2163760546","https://openalex.org/W2164060839","https://openalex.org/W4253756272"],"related_works":["https://openalex.org/W153415882","https://openalex.org/W195825275","https://openalex.org/W4312335771","https://openalex.org/W2389121573","https://openalex.org/W2500993308","https://openalex.org/W2142061179","https://openalex.org/W960957809","https://openalex.org/W4386770668","https://openalex.org/W3202246994","https://openalex.org/W69674019"],"abstract_inverted_index":{"Many":[0],"computational":[1],"problems":[2],"widely":[3],"encountered":[4],"in":[5,69],"scientific":[6],"and":[7,29,47,75,118],"engineering":[8],"applications":[9],"could":[10,51,85],"finally":[11],"be":[12,52],"transformed":[13],"to":[14],"the":[15,95,101,112],"online":[16,102,124],"linear-equations":[17],"solving.":[18],"Classic":[19],"numerical":[20],"methods":[21],"for":[22,54,122],"solving":[23,55,123],"linear":[24,57,105,129],"equations":[25],"include":[26],"Gaussian":[27],"elimination":[28],"matrix":[30],"factorization":[31],"methods,":[32],"which":[33],"are":[34],"usually":[35],"of":[36,71,80,90,104,115,128],"O(n3)":[37],"operations.":[38],"Being":[39],"important":[40],"parallel-computational":[41],"models,":[42],"both":[43,79,116],"BP":[44,59,117],"(back":[45],"propagation)":[46],"Hopfield":[48,66,119],"neural":[49,60,67,83,120],"networks":[50,84,121],"exploited":[53],"such":[56,125],"equations.":[58,106,130],"network":[61,68,72],"is":[62],"evidently":[63],"different":[64],"from":[65],"terms":[70],"definition,":[73],"architecture":[74],"learning":[76,91],"pattern.":[77],"However,":[78],"these":[81],"two":[82],"have":[86],"a":[87,126],"common":[88],"nature":[89],"(i.e.,":[92],"governed":[93],"by":[94],"same":[96],"mathematical":[97],"iteration":[98],"formula)":[99],"during":[100],"solution":[103],"In":[107],"addition,":[108],"computer-simulation":[109],"results":[110],"substantiate":[111],"theoretical":[113],"analysis":[114],"set":[127]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}