{"id":"https://openalex.org/W1972234230","doi":"https://doi.org/10.1007/s11075-012-9674-7","title":"The reflexive least squares solutions of the matrix equation $A_1X_1B_1+A_2X_2B_2+\\cdots +A_lX_lB_l=C$ with a submatrix constraint","display_name":"The reflexive least squares solutions of the matrix equation $A_1X_1B_1+A_2X_2B_2+\\cdots +A_lX_lB_l=C$ with a submatrix constraint","publication_year":2012,"publication_date":"2012-12-20","ids":{"openalex":"https://openalex.org/W1972234230","doi":"https://doi.org/10.1007/s11075-012-9674-7","mag":"1972234230"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-012-9674-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-012-9674-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5041293817","display_name":"Zhuohua Peng","orcid":"https://orcid.org/0000-0002-6026-904X"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhuohua Peng","raw_affiliation_strings":["School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, People\u2019s Republic of China","School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, People's Republic of China 411201#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, People\u2019s Republic of China","institution_ids":["https://openalex.org/I121296143"]},{"raw_affiliation_string":"School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, People's Republic of China 411201#TAB#","institution_ids":["https://openalex.org/I121296143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041293817"],"corresponding_institution_ids":["https://openalex.org/I121296143"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.0876,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.86419367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"3","first_page":"455","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9948999881744385,"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"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.7332344055175781},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6091178059577942},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5959087610244751},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.548525869846344},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5370824337005615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5176630616188049},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.41638174653053284},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3271441161632538},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29518789052963257},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.20095765590667725},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.14324772357940674},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10962465405464172},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10423555970191956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7332344055175781},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6091178059577942},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5959087610244751},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.548525869846344},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5370824337005615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5176630616188049},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.41638174653053284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3271441161632538},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29518789052963257},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.20095765590667725},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.14324772357940674},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10962465405464172},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10423555970191956},{"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},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-012-9674-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-012-9674-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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":22,"referenced_works":["https://openalex.org/W132759409","https://openalex.org/W1977350167","https://openalex.org/W1992075301","https://openalex.org/W1996383011","https://openalex.org/W2005592889","https://openalex.org/W2009607215","https://openalex.org/W2010333970","https://openalex.org/W2020995832","https://openalex.org/W2023686904","https://openalex.org/W2034621062","https://openalex.org/W2035780670","https://openalex.org/W2054539865","https://openalex.org/W2080697474","https://openalex.org/W2082219612","https://openalex.org/W2087405824","https://openalex.org/W2095771800","https://openalex.org/W2143476164","https://openalex.org/W2355306439","https://openalex.org/W2383671970","https://openalex.org/W3126588943","https://openalex.org/W4206097460","https://openalex.org/W4231424827"],"related_works":["https://openalex.org/W2807251790","https://openalex.org/W2064563243","https://openalex.org/W4250775169","https://openalex.org/W2941091020","https://openalex.org/W2799406489","https://openalex.org/W2134887131","https://openalex.org/W2028885955","https://openalex.org/W1733367267","https://openalex.org/W2810415161","https://openalex.org/W4301291886"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
