{"id":"https://openalex.org/W2276857209","doi":"https://doi.org/10.1162/neco_a_00821","title":"Recurrent Neural Network for Computing Outer Inverse","display_name":"Recurrent Neural Network for Computing Outer Inverse","publication_year":2016,"publication_date":"2016-02-19","ids":{"openalex":"https://openalex.org/W2276857209","doi":"https://doi.org/10.1162/neco_a_00821","mag":"2276857209","pmid":"https://pubmed.ncbi.nlm.nih.gov/26890345"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00821","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00821","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5005221469","display_name":"Ivan S. \u017divkovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I1338511612","display_name":"Serbian Academy of Sciences and Arts","ror":"https://ror.org/05m1y4204","country_code":"RS","type":"funder","lineage":["https://openalex.org/I1338511612"]},{"id":"https://openalex.org/I4390039372","display_name":"Mathematical Institute of the Serbian Academy of Sciences and Arts","ror":"https://ror.org/02jxk1021","country_code":null,"type":"education","lineage":["https://openalex.org/I1338511612","https://openalex.org/I4390039372"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Ivan S. \u017divkovi\u0107","raw_affiliation_strings":["Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Beograd, Serbia"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Beograd, Serbia","institution_ids":["https://openalex.org/I1338511612","https://openalex.org/I4390039372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038736735","display_name":"Predrag S. Stanimirovi\u0107","orcid":"https://orcid.org/0000-0003-0655-3741"},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Predrag S. Stanimirovi\u0107","raw_affiliation_strings":["University of Ni\u0161, Faculty of Sciences and Mathematics, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia"],"affiliations":[{"raw_affiliation_string":"University of Ni\u0161, Faculty of Sciences and Mathematics, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014988509","display_name":"Yimin Wei","orcid":"https://orcid.org/0000-0001-6192-0546"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yimin Wei","raw_affiliation_strings":["School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, P.R.C"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, P.R.C","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005221469","https://openalex.org/A5014988509","https://openalex.org/A5038736735"],"corresponding_institution_ids":["https://openalex.org/I1338511612","https://openalex.org/I152518017","https://openalex.org/I4390039372"],"apc_list":null,"apc_paid":null,"fwci":6.8556,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.96832529,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"5","first_page":"970","last_page":"998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"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":0.996999979019165,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9882000088691711,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.8448441624641418},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6635959148406982},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.6023128628730774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5930967926979065},{"id":"https://openalex.org/keywords/drazin-inverse","display_name":"Drazin inverse","score":0.5524121522903442},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5451459288597107},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49386507272720337},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49243292212486267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45491907000541687},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4247530996799469},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.3725237250328064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3591160774230957},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27603980898857117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25303077697753906},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.158765971660614},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08554816246032715}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8448441624641418},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6635959148406982},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.6023128628730774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5930967926979065},{"id":"https://openalex.org/C2777795832","wikidata":"https://www.wikidata.org/wiki/Q4521948","display_name":"Drazin inverse","level":3,"score":0.5524121522903442},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5451459288597107},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49386507272720337},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49243292212486267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45491907000541687},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4247530996799469},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3725237250328064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3591160774230957},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27603980898857117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25303077697753906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.158765971660614},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08554816246032715},{"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/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},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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":2,"locations":[{"id":"doi:10.1162/neco_a_00821","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00821","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:26890345","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26890345","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W63662626","https://openalex.org/W564684706","https://openalex.org/W604917427","https://openalex.org/W1530239534","https://openalex.org/W1578642671","https://openalex.org/W1964693520","https://openalex.org/W1975062715","https://openalex.org/W1978400376","https://openalex.org/W1984864449","https://openalex.org/W1986219847","https://openalex.org/W1986337835","https://openalex.org/W1991717161","https://openalex.org/W1996208176","https://openalex.org/W1997270899","https://openalex.org/W1998304734","https://openalex.org/W1999054923","https://openalex.org/W2001629397","https://openalex.org/W2010411578","https://openalex.org/W2011170491","https://openalex.org/W2013066794","https://openalex.org/W2022132163","https://openalex.org/W2027967385","https://openalex.org/W2033935789","https://openalex.org/W2034514780","https://openalex.org/W2052197050","https://openalex.org/W2052234213","https://openalex.org/W2052528893","https://openalex.org/W2055576996","https://openalex.org/W2055610189","https://openalex.org/W2077639421","https://openalex.org/W2080220726","https://openalex.org/W2088026800","https://openalex.org/W2094992879","https://openalex.org/W2100748202","https://openalex.org/W2130317597","https://openalex.org/W2138244240","https://openalex.org/W2198164043","https://openalex.org/W2326916722","https://openalex.org/W2340966007","https://openalex.org/W2798813531"],"related_works":["https://openalex.org/W2379864855","https://openalex.org/W1978110282","https://openalex.org/W2950418012","https://openalex.org/W2945629520","https://openalex.org/W2964125203","https://openalex.org/W4220858424","https://openalex.org/W2521026157","https://openalex.org/W2379705405","https://openalex.org/W2007635291","https://openalex.org/W2207279359"],"abstract_inverted_index":{"Two":[0],"linear":[1],"recurrent":[2,21],"neural":[3,22,113],"networks":[4,23],"for":[5,38],"generating":[6],"outer":[7],"inverses":[8,102],"with":[9],"prescribed":[10],"range":[11],"and":[12],"null":[13],"space":[14],"are":[15,103,115],"defined.":[16,104],"Each":[17],"of":[18,33,55,61,70,73,87,91,110,122],"the":[19,27,39,43,49,53,62,68,71,77,85,89,98,111,120],"proposed":[20,36,112],"is":[24,65],"based":[25],"on":[26],"matrix-valued":[28],"differential":[29],"equation,":[30],"a":[31,74],"generalization":[32],"dynamic":[34],"equations":[35],"earlier":[37],"nonsingular":[40],"matrix":[41,92],"inversion,":[42,45,51],"Moore-Penrose":[44],"as":[46,48],"well":[47],"Drazin":[50],"under":[52],"condition":[54],"zero":[56],"initial":[57],"state.":[58],"The":[59,94,105],"application":[60],"first":[63],"approach":[64,79],"conditioned":[66],"by":[67],"properties":[69],"spectrum":[72],"certain":[75],"matrix;":[76],"second":[78],"eliminates":[80],"this":[81],"drawback,":[82],"though":[83],"at":[84],"cost":[86],"increasing":[88],"number":[90],"operations.":[93],"cases":[95],"corresponding":[96],"to":[97],"most":[99],"common":[100],"generalized":[101],"conditions":[106],"that":[107],"ensure":[108],"stability":[109],"network":[114],"presented.":[116],"Illustrative":[117],"examples":[118],"present":[119],"results":[121],"numerical":[123],"simulations.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}