{"id":"https://openalex.org/W1558614921","doi":"https://doi.org/10.1155/2012/492951","title":"An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations <i>AXB</i> = <i>E</i>, <i>CXD</i> = <i>F</i>","display_name":"An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations <i>AXB</i> = <i>E</i>, <i>CXD</i> = <i>F</i>","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1558614921","doi":"https://doi.org/10.1155/2012/492951","mag":"1558614921"},"language":"en","primary_location":{"id":"doi:10.1155/2012/492951","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/492951","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/492951.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/2012/492951.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009672167","display_name":"Deqin Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Deqin Chen","raw_affiliation_strings":["School of Science, Sichuan University of Science and Engineering, Zigong 643000"],"affiliations":[{"raw_affiliation_string":"School of Science, Sichuan University of Science and Engineering, Zigong 643000","institution_ids":["https://openalex.org/I64852412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100696176","display_name":"Feng Yin","orcid":"https://orcid.org/0000-0002-6729-4205"},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Yin","raw_affiliation_strings":["School of Science, Sichuan University of Science and Engineering, Zigong 643000, China","School of Science, Sichuan University of Science and Engineering, Zigong 643000"],"affiliations":[{"raw_affiliation_string":"School of Science, Sichuan University of Science and Engineering, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]},{"raw_affiliation_string":"School of Science, Sichuan University of Science and Engineering, Zigong 643000","institution_ids":["https://openalex.org/I64852412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103141914","display_name":"Guang-Xin Huang","orcid":"https://orcid.org/0000-0003-3220-3083"},"institutions":[{"id":"https://openalex.org/I31595395","display_name":"Chengdu University of Technology","ror":"https://ror.org/05pejbw21","country_code":"CN","type":"education","lineage":["https://openalex.org/I31595395"]},{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guang-Xin Huang","raw_affiliation_strings":["College of Management Science, Key Laboratory of Geomathematics in Sichuan, Chengdu University of Technology, Chengdu 610059, China","School of Science, Sichuan University of Science and Engineering, Zigong 643000, China","College of Management Science, \n                    Key Laboratory of Geomathematics in Sichuan, Chengdu University of Technology, Chengdu 610059"],"affiliations":[{"raw_affiliation_string":"College of Management Science, Key Laboratory of Geomathematics in Sichuan, Chengdu University of Technology, Chengdu 610059, China","institution_ids":["https://openalex.org/I31595395"]},{"raw_affiliation_string":"School of Science, Sichuan University of Science and Engineering, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]},{"raw_affiliation_string":"College of Management Science, \n                    Key Laboratory of Geomathematics in Sichuan, Chengdu University of Technology, Chengdu 610059","institution_ids":["https://openalex.org/I31595395"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009672167"],"corresponding_institution_ids":["https://openalex.org/I64852412"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.0217,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85740607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2012","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9747999906539917,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9575999975204468,"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/algorithm","display_name":"Algorithm","score":0.6598227024078369},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33021634817123413}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6598227024078369},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33021634817123413}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/492951","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/492951","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/492951.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/1355495209","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495209","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:doaj.org/article:b7bf759baa7a4215ba2badaca1db55e4","is_oa":true,"landing_page_url":"https://doaj.org/article/b7bf759baa7a4215ba2badaca1db55e4","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/492951","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/492951","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/492951.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":[{"id":"https://openalex.org/G2460478950","display_name":null,"funder_award_id":"12ZB289","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G3815998098","display_name":null,"funder_award_id":"2010XJKYL018","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G5179239235","display_name":null,"funder_award_id":"12ZA008","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G5970465578","display_name":null,"funder_award_id":"scsxdz2011005","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320322947","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23"},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1558614921.pdf","grobid_xml":"https://content.openalex.org/works/W1558614921.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W54669653","https://openalex.org/W437003251","https://openalex.org/W1664553927","https://openalex.org/W1971734187","https://openalex.org/W2001090660","https://openalex.org/W2009435862","https://openalex.org/W2012738485","https://openalex.org/W2013614475","https://openalex.org/W2014548081","https://openalex.org/W2014735964","https://openalex.org/W2017891382","https://openalex.org/W2030452782","https://openalex.org/W2033966841","https://openalex.org/W2039408173","https://openalex.org/W2040534832","https://openalex.org/W2041705422","https://openalex.org/W2043218140","https://openalex.org/W2047017077","https://openalex.org/W2050500034","https://openalex.org/W2060899753","https://openalex.org/W2062691903","https://openalex.org/W2068124938","https://openalex.org/W2075226287","https://openalex.org/W2077269325","https://openalex.org/W2077367373","https://openalex.org/W2082219612","https://openalex.org/W2082674017","https://openalex.org/W2082820235","https://openalex.org/W2094758737","https://openalex.org/W2095771800","https://openalex.org/W2113888168","https://openalex.org/W2127642592","https://openalex.org/W2128142781","https://openalex.org/W2388871042","https://openalex.org/W3145077270","https://openalex.org/W7010844525"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"An":[0],"iterative":[1,58,72,76,89,103,161],"algorithm":[2,73,162],"is":[3,45,105,163],"constructed":[4],"to":[5,157],"solve":[6],"the":[7,30,63,71,79,92,108,137],"linear":[8],"matrix":[9,26,31,50,59,93,104,129,146],"equation":[10,32,94,147],"pair":[11,33,95,148],"A":[12,34,113],"X":[13,19,27,35,41,51,60,114,120,130],"B":[14,36,115],"=":[15,21,37,43,116,122],"E":[16,38,117],",":[17,39,52,62,118],"C":[18,40,119],"D":[20,42,121],"F":[22,44,123],"over":[23,47],"generalized":[24,48,55,64,87,127,139],"reflexive":[25,49,56,65,88,128,140],".":[28,150],"When":[29],"consistent":[46],"for":[53,124],"any":[54],"initial":[57,102],"1":[61],"solution":[66,90,111,141],"can":[67,96,132],"be":[68,97,133],"obtained":[69],"by":[70,135],"within":[74],"finite":[75],"steps":[77],"in":[78],"absence":[80],"of":[81,91,112,142],"round\u2010off":[82],"errors.":[83],"The":[84],"unique":[85],"least\u2010norm":[86,138],"derived":[98,134],"when":[99],"an":[100],"appropriate":[101],"chosen.":[106],"Furthermore,":[107],"optimal":[109],"approximate":[110],"a":[125,143],"given":[126,156],"0":[131],"finding":[136],"new":[144],"corresponding":[145],"with":[149],"Finally,":[151],"several":[152],"numerical":[153],"examples":[154],"are":[155],"illustrate":[158],"that":[159],"our":[160],"effective.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
