{"id":"https://openalex.org/W1966353092","doi":"https://doi.org/10.1155/2013/597628","title":"Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices","display_name":"Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1966353092","doi":"https://doi.org/10.1155/2013/597628","mag":"1966353092"},"language":"en","primary_location":{"id":"doi:10.1155/2013/597628","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/597628","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/597628.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/597628.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073496790","display_name":"Xiongfei Zou","orcid":"https://orcid.org/0000-0002-7343-7508"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiongfei Zou","raw_affiliation_strings":["School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017168501","display_name":"Ying Tang","orcid":"https://orcid.org/0000-0002-6063-4481"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Tang","raw_affiliation_strings":["School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074669175","display_name":"Shirong Bu","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shirong Bu","raw_affiliation_strings":["School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111808741","display_name":"Zhengxiang Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengxiang Luo","raw_affiliation_strings":["School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034087989","display_name":"Shouming Zhong","orcid":"https://orcid.org/0000-0002-0334-6117"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shouming Zhong","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5073496790"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.4941,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74959143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"13"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8431968688964844},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5861386656761169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5563706159591675},{"id":"https://openalex.org/keywords/normal-matrix","display_name":"Normal matrix","score":0.5453829169273376},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.5190120935440063},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5155141353607178},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4504191279411316},{"id":"https://openalex.org/keywords/modal-matrix","display_name":"Modal matrix","score":0.4490474462509155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4461650252342224},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39739885926246643},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3078489899635315},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.29464191198349},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27952516078948975},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.21106785535812378},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17108619213104248},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.08486106991767883}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8431968688964844},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5861386656761169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5563706159591675},{"id":"https://openalex.org/C175380299","wikidata":"https://www.wikidata.org/wiki/Q6852339","display_name":"Normal matrix","level":3,"score":0.5453829169273376},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.5190120935440063},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5155141353607178},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4504191279411316},{"id":"https://openalex.org/C73772418","wikidata":"https://www.wikidata.org/wiki/Q6888018","display_name":"Modal matrix","level":5,"score":0.4490474462509155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4461650252342224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39739885926246643},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3078489899635315},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29464191198349},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27952516078948975},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.21106785535812378},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17108619213104248},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.08486106991767883},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/597628","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/597628","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/597628.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394807894","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394807894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:597628","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/597628.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:3f7c00521575425795d281fa5b389996","is_oa":true,"landing_page_url":"https://doaj.org/article/3f7c00521575425795d281fa5b389996","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/597628","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/597628","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/597628.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1966353092.pdf","grobid_xml":"https://content.openalex.org/works/W1966353092.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W5731987","https://openalex.org/W14550888","https://openalex.org/W1968014618","https://openalex.org/W1970923936","https://openalex.org/W1980793158","https://openalex.org/W1987113808","https://openalex.org/W1997442072","https://openalex.org/W1998767583","https://openalex.org/W1998790013","https://openalex.org/W2008073635","https://openalex.org/W2016491762","https://openalex.org/W2025433865","https://openalex.org/W2038754956","https://openalex.org/W2057255661","https://openalex.org/W2090902788","https://openalex.org/W2092103935","https://openalex.org/W2095657361","https://openalex.org/W2101219687","https://openalex.org/W2132450099","https://openalex.org/W2139095575","https://openalex.org/W2145356049","https://openalex.org/W2159706417","https://openalex.org/W2166604943","https://openalex.org/W2167002981","https://openalex.org/W2317300004","https://openalex.org/W4254543305"],"related_works":["https://openalex.org/W3127622694","https://openalex.org/W4377200779","https://openalex.org/W105179031","https://openalex.org/W2092103935","https://openalex.org/W2955282717","https://openalex.org/W2117499033","https://openalex.org/W209453833","https://openalex.org/W4251966336","https://openalex.org/W2030060230","https://openalex.org/W2077030276"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3],"novel":[4],"neural-network-based":[5],"approach":[6],"for":[7],"extracting":[8,88],"some":[9],"eigenpairs":[10],"of":[11,15,38,90,99,114],"real":[12,33,82,92,100],"normal":[13,101],"matrices":[14,93,102],"order":[16],"n":[17,65,72,80],".":[18],"Based":[19],"on":[20,56],"the":[21,24,28,48,52,105,111,115],"proposed":[22,59,116],"algorithm,":[23],"eigenvalues":[25],"that":[26,76,87],"have":[27],"largest":[29],"and":[30],"smallest":[31],"modulus,":[32],"parts,":[34],"or":[35],"absolute":[36],"values":[37],"imaginary":[39],"parts":[40],"can":[41,68,94],"be":[42,95],"extracted,":[43],"respectively,":[44],"as":[45,47],"well":[46],"corresponding":[49],"eigenvectors.":[50],"Although":[51],"ordinary":[53],"differential":[54],"equation":[55],"which":[57],"our":[58],"algorithm":[60],"is":[61,63],"built":[62],"only":[64],"-dimensional,":[66],"it":[67],"succeed":[69],"to":[70,97],"extract":[71],"-dimensional":[73,81],"complex":[74],"eigenvectors":[75],"are":[77],"indeed":[78],"2":[79],"vectors.":[83],"Moreover,":[84],"we":[85],"show":[86],"eigen-pairs":[89],"general":[91],"reduced":[96],"those":[98],"by":[103],"employing":[104],"norm-reducing":[106],"skill.":[107],"Numerical":[108],"experiments":[109],"verified":[110],"computational":[112],"capability":[113],"algorithm.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}