{"id":"https://openalex.org/W4393033495","doi":"https://doi.org/10.1109/tsmc.2024.3370636","title":"Comprehensive Study on Zeroing Neural Network With High-Order Evolutionary Formula, Nonlinear Functions, and Variable Parameter for Time-Changing Matrix Cholesky Decomposition","display_name":"Comprehensive Study on Zeroing Neural Network With High-Order Evolutionary Formula, Nonlinear Functions, and Variable Parameter for Time-Changing Matrix Cholesky Decomposition","publication_year":2024,"publication_date":"2024-03-21","ids":{"openalex":"https://openalex.org/W4393033495","doi":"https://doi.org/10.1109/tsmc.2024.3370636"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2024.3370636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2024.3370636","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","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/A5005130812","display_name":"Lin Xiao","orcid":"https://orcid.org/0000-0003-3172-3490"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lin Xiao","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113148425","display_name":"Sida Xiao","orcid":null},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sida Xiao","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101577827","display_name":"Yongjun He","orcid":"https://orcid.org/0000-0002-5228-0302"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongjun He","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070031719","display_name":"Jianhua Dai","orcid":"https://orcid.org/0000-0003-1459-0833"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianhua Dai","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025640070","display_name":"Yaonan Wang","orcid":"https://orcid.org/0000-0002-0519-6458"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaonan Wang","raw_affiliation_strings":["College of Electric and Information Technology, Hunan University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"College of Electric and Information Technology, Hunan University, Changsha, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100633409","display_name":"Yiwei Li","orcid":"https://orcid.org/0000-0002-8380-4164"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiwei Li","raw_affiliation_strings":["College of Computer, National University of Defense Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"College of Computer, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5005130812"],"corresponding_institution_ids":["https://openalex.org/I173759888"],"apc_list":null,"apc_paid":null,"fwci":2.2521,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86695533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"54","issue":"6","first_page":"3642","last_page":"3651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.989300012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.9852278232574463},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.8680060505867004},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6404874324798584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5934656858444214},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5898524522781372},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5179623365402222},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.517702579498291},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.4884904623031616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47291573882102966},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4495934545993805},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.44741880893707275},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.43436384201049805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3822650909423828},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1070636510848999},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07872787117958069},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06728100776672363}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9852278232574463},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.8680060505867004},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6404874324798584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5934656858444214},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5898524522781372},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5179623365402222},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.517702579498291},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.4884904623031616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47291573882102966},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4495934545993805},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.44741880893707275},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.43436384201049805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3822650909423828},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1070636510848999},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07872787117958069},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06728100776672363},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2024.3370636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2024.3370636","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G268291241","display_name":null,"funder_award_id":"2021JJ20005","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5166635775","display_name":null,"funder_award_id":"61866013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7738513684","display_name":null,"funder_award_id":"2022RC1103","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1539521189","https://openalex.org/W1968527606","https://openalex.org/W1974942521","https://openalex.org/W1993293661","https://openalex.org/W2054141820","https://openalex.org/W2072175279","https://openalex.org/W2095590702","https://openalex.org/W2112447569","https://openalex.org/W2126082093","https://openalex.org/W2130317597","https://openalex.org/W2133702739","https://openalex.org/W2411208350","https://openalex.org/W2727575785","https://openalex.org/W2791809365","https://openalex.org/W2793464405","https://openalex.org/W2799458759","https://openalex.org/W2806365404","https://openalex.org/W2891576042","https://openalex.org/W2896377848","https://openalex.org/W2899417080","https://openalex.org/W2915648089","https://openalex.org/W2965637422","https://openalex.org/W2968043153","https://openalex.org/W2971039702","https://openalex.org/W2990029213","https://openalex.org/W2992236792","https://openalex.org/W3000352647","https://openalex.org/W3012462771","https://openalex.org/W3016899151","https://openalex.org/W3082300084","https://openalex.org/W3083648248","https://openalex.org/W3094568852","https://openalex.org/W3120595940","https://openalex.org/W3121297827","https://openalex.org/W3125398343","https://openalex.org/W3142053154","https://openalex.org/W3155208883","https://openalex.org/W3169126409","https://openalex.org/W3169672010","https://openalex.org/W3172024907","https://openalex.org/W3174840197","https://openalex.org/W3202414904","https://openalex.org/W4210375380","https://openalex.org/W4213015918","https://openalex.org/W4224042789","https://openalex.org/W4224249946","https://openalex.org/W4245345046","https://openalex.org/W4377971431","https://openalex.org/W6676727762"],"related_works":["https://openalex.org/W2504688771","https://openalex.org/W4255359805","https://openalex.org/W2075453197","https://openalex.org/W63685308","https://openalex.org/W2057318281","https://openalex.org/W2233293187","https://openalex.org/W2924783966","https://openalex.org/W1482750774","https://openalex.org/W2394244817","https://openalex.org/W2122238092"],"abstract_inverted_index":{"In":[0,48],"this":[1],"article,":[2],"a":[3,9,14,50],"low-order":[4],"zeroing":[5],"neural":[6],"network":[7],"(LZNN),":[8],"high-order":[10,44],"ZNN":[11,16],"(HZNN),":[12],"and":[13,20,34,43,61,68,73,102,110],"variable-parameter":[15],"(VZNN)":[17],"are":[18,37],"designed":[19],"applied":[21,56],"to":[22,57,64,127,130],"the":[23,32,41,58,66,71,78,87,118,122,131,138],"time-changing":[24,88],"Cholesky":[25,89,135],"decomposition":[26,90,136],"of":[27,92,108,121,134,140],"any":[28,93],"positive-definite":[29,94],"matrix,":[30,95],"where":[31],"LZNN":[33,72],"HZNN":[35,74],"models":[36,63,75],"generated":[38],"based":[39],"on":[40],"traditional":[42],"evolutionary":[45],"formulas,":[46],"respectively.":[47],"addition,":[49],"new":[51],"activation":[52],"function":[53],"(N-Acf)":[54],"is":[55,97,125],"LZNN,":[59],"HZNN,":[60],"VZNN":[62,123],"improve":[65],"convergence":[67,83,129],"robustness.":[69],"Importantly,":[70],"activated":[76],"by":[77],"N-Acf":[79],"have":[80],"faster":[81],"predefined-time":[82],"velocity":[84],"when":[85],"solving":[86],"problem":[91],"which":[96],"demonstrated":[98],"via":[99],"theoretical":[100,111,132],"analysis":[101],"numerical":[103],"experiments.":[104],"Finally,":[105],"in":[106],"light":[107],"empirical":[109],"evidence,":[112],"it":[113],"can":[114],"be":[115],"established":[116],"that":[117],"solution":[119,133],"model":[120,124],"able":[126],"undergo":[128],"despite":[137],"presence":[139],"interposing":[141],"noise.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}