{"id":"https://openalex.org/W1992075301","doi":"https://doi.org/10.1137/s0895479803434185","title":"The Inverse Eigenproblem of Centrosymmetric Matrices with a Submatrix Constraint and Its Approximation","display_name":"The Inverse Eigenproblem of Centrosymmetric Matrices with a Submatrix Constraint and Its Approximation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1992075301","doi":"https://doi.org/10.1137/s0895479803434185","mag":"1992075301"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479803434185","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803434185","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5055283405","display_name":"Zheng\u2010Jian Bai","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zheng-Jian Bai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055283405"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0541,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.7559715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"4","first_page":"1100","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8088093996047974},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7671073079109192},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6833193898200989},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6109987497329712},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5889316201210022},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5786613821983337},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45669370889663696},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.44924870133399963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21000808477401733},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08361926674842834}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8088093996047974},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7671073079109192},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6833193898200989},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6109987497329712},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5889316201210022},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5786613821983337},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45669370889663696},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.44924870133399963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21000808477401733},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08361926674842834},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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:10.1137/s0895479803434185","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803434185","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/130437","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/130437","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W54669653","https://openalex.org/W573151571","https://openalex.org/W1556970733","https://openalex.org/W1970514593","https://openalex.org/W1977685916","https://openalex.org/W1984869715","https://openalex.org/W1991136704","https://openalex.org/W1992032371","https://openalex.org/W1995565421","https://openalex.org/W2014975345","https://openalex.org/W2016127945","https://openalex.org/W2016162463","https://openalex.org/W2020376719","https://openalex.org/W2063492807","https://openalex.org/W2080097309","https://openalex.org/W2084876298","https://openalex.org/W2095766105","https://openalex.org/W2115113403","https://openalex.org/W2143775470","https://openalex.org/W2144181355","https://openalex.org/W2161216573","https://openalex.org/W2171868138","https://openalex.org/W2195864291","https://openalex.org/W2314588574","https://openalex.org/W4249026422"],"related_works":["https://openalex.org/W2366593309","https://openalex.org/W4205336553","https://openalex.org/W3205368572","https://openalex.org/W151283020","https://openalex.org/W2358778982","https://openalex.org/W2026922797","https://openalex.org/W4210447084","https://openalex.org/W1498028334","https://openalex.org/W2120227340","https://openalex.org/W4235706696"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"first":[4],"consider":[5],"the":[6,10,14,17,53,67,79,84,108,111,117,126,139],"existence":[7],"of":[8,27,34,58,71],"and":[9,31,38,62,64,69,121,134],"general":[11],"expression":[12],"for":[13,83],"solution":[15,89,109,133],"to":[16,110,138],"constrained":[18,85,112],"inverse":[19,86,113],"eigenproblem":[20],"defined":[21],"as":[22],"follows:":[23],"given":[24,95],"a":[25,32,103,135],"set":[26,33,90],"complex":[28,35],"n-vectors":[29],"$\\{\\bx_i\\}_{i=1}^{m}$":[30,63],"numbers":[36],"$\\{\\la_i\\}_{i=1}^m$,":[37],"an":[39,45,96,131],"s-by-s":[40,54],"real":[41,47,98],"matrix":[42,49,100,104],"$C_0$,":[43,61],"find":[44,102],"n-by-n":[46,99],"centrosymmetric":[48],"C":[50,59,105,120],"such":[51,115],"that":[52,116],"leading":[55],"principal":[56],"submatrix":[57],"is":[60,91,107,123],"$\\{\\la_i\\}_{i=1}^m$":[65],"are":[66,75,146],"eigenvectors":[68],"eigenvalues":[70],"C,":[72],"respectively.":[73],"We":[74,129],"then":[76],"concerned":[77],"with":[78],"best":[80,140],"approximation":[81,141],"problem":[82,87,114],"whose":[88],"nonempty.":[92],"That":[93],"is,":[94],"arbitrary":[97],"$\\tilde{C}$,":[101],"which":[106],"distance":[118],"between":[119],"$\\tilde{C}$":[122],"minimized":[124],"in":[125],"Frobenius":[127],"norm.":[128],"give":[130],"explicit":[132],"numerical":[136],"algorithm":[137],"problem.":[142],"Some":[143],"illustrative":[144],"experiments":[145],"also":[147],"presented.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
