{"id":"https://openalex.org/W7118187994","doi":"https://doi.org/10.1007/s40314-025-03583-3","title":"A canonical form of Greville\u2019s spectral $$\\{1,2,3\\}$$-inverse with applications","display_name":"A canonical form of Greville\u2019s spectral $$\\{1,2,3\\}$$-inverse with applications","publication_year":2026,"publication_date":"2026-01-05","ids":{"openalex":"https://openalex.org/W7118187994","doi":"https://doi.org/10.1007/s40314-025-03583-3"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03583-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-025-03583-3","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5020097420","display_name":"Cang Wu","orcid":"https://orcid.org/0000-0002-5487-6361"},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cang Wu","raw_affiliation_strings":["College of Science, Nanjing Forestry University, 210037, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Nanjing Forestry University, 210037, Nanjing, China","institution_ids":["https://openalex.org/I167027274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001363392","display_name":"DIJANA MOSIC","orcid":null},"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":false,"raw_author_name":"Dijana Mosi\u0107","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Ni\u0161, 18000, Ni\u0161, Serbia"],"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Ni\u0161, 18000, Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047126466","display_name":"Guiqi Shi","orcid":"https://orcid.org/0000-0002-8470-718X"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]},{"id":"https://openalex.org/I4210116001","display_name":"Guiyang University","ror":"https://ror.org/025edj240","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210116001"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guiqi Shi","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, 550025, Guiyang, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, 550025, Guiyang, China","institution_ids":["https://openalex.org/I178232147","https://openalex.org/I4210116001"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047126466"],"corresponding_institution_ids":["https://openalex.org/I178232147","https://openalex.org/I4210116001"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05635536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9805999994277954,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9805999994277954,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.00279999990016222,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.5831999778747559},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"Spectral properties","score":0.5593000054359436},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5343999862670898},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5281999707221985},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5040000081062317},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4625000059604645},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.43290001153945923},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.3743000030517578},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.3691999912261963}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6952999830245972},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.5831999778747559},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.5593000054359436},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5343999862670898},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5281999707221985},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4625000059604645},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3637999892234802},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.34599998593330383},{"id":"https://openalex.org/C21556879","wikidata":"https://www.wikidata.org/wiki/Q43219517","display_name":"Moore\u2013Penrose pseudoinverse","level":3,"score":0.33799999952316284},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.33719998598098755},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.33090001344680786},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.32919999957084656},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.32089999318122864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31839999556541443},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C61987429","wikidata":"https://www.wikidata.org/wiki/Q3064355","display_name":"M-matrix","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26499998569488525},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.258899986743927},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C86761442","wikidata":"https://www.wikidata.org/wiki/Q6787879","display_name":"Matrix method","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.2506999969482422},{"id":"https://openalex.org/C122129529","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse system","level":3,"score":0.25}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03583-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-025-03583-3","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1970616089","https://openalex.org/W1974511160","https://openalex.org/W2019498037","https://openalex.org/W2021784463","https://openalex.org/W2044507174","https://openalex.org/W2057818040","https://openalex.org/W2093032237","https://openalex.org/W2165942041","https://openalex.org/W2322753244","https://openalex.org/W2471807377","https://openalex.org/W2798427052","https://openalex.org/W2883458605","https://openalex.org/W2921775510","https://openalex.org/W2922894488","https://openalex.org/W2968901074","https://openalex.org/W3083179437","https://openalex.org/W3095978713","https://openalex.org/W3108627397","https://openalex.org/W3119821756","https://openalex.org/W3127222251","https://openalex.org/W3147272950","https://openalex.org/W4292295077","https://openalex.org/W4391069561","https://openalex.org/W4400039068","https://openalex.org/W4400277932","https://openalex.org/W4410834626"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-01-08T20:05:33.558190","created_date":"2026-01-05T00:00:00"}