{"id":"https://openalex.org/W7166723169","doi":"https://doi.org/10.1007/s10444-026-10324-5","title":"Randomized gradient descent method for solving the large-scale inverse eigenvalue problem arising from the fractional order control system","display_name":"Randomized gradient descent method for solving the large-scale inverse eigenvalue problem arising from the fractional order control system","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7166723169","doi":"https://doi.org/10.1007/s10444-026-10324-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10324-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10324-5","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","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/A5016966395","display_name":"Bin-Xin He","orcid":null},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin-Xin He","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China","Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen, 518110, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen, 518110, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139652458","display_name":"Hao Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hao Liu","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China","Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen, 518110, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen, 518110, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065870160","display_name":"X J Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I82760581","display_name":"Taizhou University","ror":"https://ror.org/04fzhyx73","country_code":"CN","type":"education","lineage":["https://openalex.org/I82760581"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao-Ping Chen","raw_affiliation_strings":["Department of Mathematics, Taizhou University, Taizhou, 225300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taizhou University, Taizhou, 225300, China","institution_ids":["https://openalex.org/I82760581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065870160","https://openalex.org/A5139652458"],"corresponding_institution_ids":["https://openalex.org/I82760581","https://openalex.org/I9842412"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.83206695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.27059999108314514,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.27059999108314514,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.16920000314712524,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.09210000187158585,"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":0.6647999882698059},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5680999755859375},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.5393999814987183},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5077999830245972},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4742000102996826},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.46860000491142273},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.45750001072883606},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4562999904155731}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6884999871253967},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6647999882698059},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5680999755859375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5404000282287598},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.5393999814987183},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5077999830245972},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.46860000491142273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46549999713897705},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.2896000146865845},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.26660001277923584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-026-10324-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10324-5","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.9064309597015381,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1417089787","display_name":null,"funder_award_id":"11571171","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2449008833","display_name":null,"funder_award_id":"JCYJ20230807142002006","funder_id":"https://openalex.org/F4320336569","funder_display_name":"Shenzhen Science and Technology Innovation Program"},{"id":"https://openalex.org/G8681036395","display_name":null,"funder_award_id":"11401305","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336569","display_name":"Shenzhen Science and Technology Innovation Program","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W2013207196","https://openalex.org/W2051244075","https://openalex.org/W2054677627","https://openalex.org/W2091306590","https://openalex.org/W2112223587","https://openalex.org/W2146115574","https://openalex.org/W2147950119","https://openalex.org/W2171052646","https://openalex.org/W2477921776","https://openalex.org/W2593459665","https://openalex.org/W2763081248","https://openalex.org/W2790998159","https://openalex.org/W2793070439","https://openalex.org/W2883277610","https://openalex.org/W2923102530","https://openalex.org/W2937486991","https://openalex.org/W2941712671","https://openalex.org/W2963433607","https://openalex.org/W2963941964","https://openalex.org/W2994760360","https://openalex.org/W3007713149","https://openalex.org/W3081544358","https://openalex.org/W3095761189","https://openalex.org/W3107451544","https://openalex.org/W3212510276","https://openalex.org/W4213348416","https://openalex.org/W4223980847","https://openalex.org/W4245345046","https://openalex.org/W4301223505","https://openalex.org/W4303446428","https://openalex.org/W4316039513","https://openalex.org/W4372312017","https://openalex.org/W4381384257","https://openalex.org/W4384025270","https://openalex.org/W4389684850","https://openalex.org/W4407303621","https://openalex.org/W4410230756","https://openalex.org/W4410581531","https://openalex.org/W4413801600","https://openalex.org/W4414010644","https://openalex.org/W4414223436","https://openalex.org/W4414286185"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-07-01T00:00:00"}
