{"id":"https://openalex.org/W1982463462","doi":"https://doi.org/10.1155/2014/954523","title":"A Modified Gradient Based Algorithm for Solving Matrix Equations<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>D</mml:mi><mml:mi mathvariant=\"normal\"/><mml:mo>=</mml:mo><mml:mi>F</mml:mi></mml:math>","display_name":"A Modified Gradient Based Algorithm for Solving Matrix Equations<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>D</mml:mi><mml:mi mathvariant=\"normal\"/><mml:mo>=</mml:mo><mml:mi>F</mml:mi></mml:math>","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1982463462","doi":"https://doi.org/10.1155/2014/954523","mag":"1982463462"},"language":"lv","primary_location":{"id":"doi:10.1155/2014/954523","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/954523","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/954523.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/2014/954523.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040384643","display_name":"Kanmin Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I134626604","display_name":"Jiujiang University","ror":"https://ror.org/0066vpg85","country_code":"CN","type":"education","lineage":["https://openalex.org/I134626604"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kanmin Wang","raw_affiliation_strings":["Department of Mathematics, Jiujiang University, Jiujiang 332005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiujiang University, Jiujiang 332005, China","institution_ids":["https://openalex.org/I134626604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047500141","display_name":"Zhibing Liu","orcid":"https://orcid.org/0000-0002-7429-6137"},"institutions":[{"id":"https://openalex.org/I134626604","display_name":"Jiujiang University","ror":"https://ror.org/0066vpg85","country_code":"CN","type":"education","lineage":["https://openalex.org/I134626604"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhibing Liu","raw_affiliation_strings":["Department of Mathematics, Jiujiang University, Jiujiang 332005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiujiang University, Jiujiang 332005, China","institution_ids":["https://openalex.org/I134626604"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109674531","display_name":"Chengfeng Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I134626604","display_name":"Jiujiang University","ror":"https://ror.org/0066vpg85","country_code":"CN","type":"education","lineage":["https://openalex.org/I134626604"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengfeng Xu","raw_affiliation_strings":["Department of Mathematics, Jiujiang University, Jiujiang 332005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiujiang University, Jiujiang 332005, China","institution_ids":["https://openalex.org/I134626604"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047500141"],"corresponding_institution_ids":["https://openalex.org/I134626604"],"apc_list":{"value":1025,"currency":"USD","value_usd":1050},"apc_paid":{"value":1025,"currency":"USD","value_usd":1050},"fwci":0.3493,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61131907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"6"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976000189781189,"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":0.9889000058174133,"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/algorithm","display_name":"Algorithm","score":0.7098528146743774},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5203115940093994}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7098528146743774},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5203115940093994}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2014/954523","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/954523","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/954523.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/1425305565","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305565","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:e9e7349da4e04665951f9fad7e42ef2b","is_oa":false,"landing_page_url":"https://doaj.org/article/e9e7349da4e04665951f9fad7e42ef2b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/954523","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/954523","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/954523.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1982463462.pdf","grobid_xml":"https://content.openalex.org/works/W1982463462.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1978922993","https://openalex.org/W1979278406","https://openalex.org/W1996271504","https://openalex.org/W2002436765","https://openalex.org/W2005691328","https://openalex.org/W2008233371","https://openalex.org/W2010954562","https://openalex.org/W2023660467","https://openalex.org/W2025749634","https://openalex.org/W2029441975","https://openalex.org/W2031000778","https://openalex.org/W2033029203","https://openalex.org/W2049871086","https://openalex.org/W2054689585","https://openalex.org/W2056478390","https://openalex.org/W2056615320","https://openalex.org/W2063984680","https://openalex.org/W2066021453","https://openalex.org/W2072281876","https://openalex.org/W2081128548","https://openalex.org/W2088748973","https://openalex.org/W2105828609","https://openalex.org/W2106746318","https://openalex.org/W2121863229","https://openalex.org/W2138844572","https://openalex.org/W2168947999","https://openalex.org/W2186686947","https://openalex.org/W3140368695"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W3141679561"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"develop":[4],"a":[5],"modified":[6],"gradient":[7,20],"based":[8,21],"algorithm":[9],"for":[10],"solving":[11],"matrix":[12],"equations<mml:math":[13],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14],"id=\"M2\"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>D</mml:mi><mml:mi":[15],"mathvariant=\"normal\"/><mml:mo>=</mml:mo><mml:mi>F</mml:mi></mml:math>.":[16],"Different":[17],"from":[18],"the":[19,29,33,44,51,64,67],"method":[22,53],"introduced":[23],"by":[24],"Xie":[25],"et":[26],"al.,":[27],"2010,":[28],"information":[30],"generated":[31],"in":[32],"first":[34],"half-iterative":[35],"step":[36],"is":[37],"fully":[38],"exploited":[39],"and":[40],"used":[41],"to":[42,62],"construct":[43],"approximate":[45],"solution.":[46],"Theoretical":[47],"analysis":[48],"shows":[49],"that":[50],"new":[52,68],"converges":[54],"under":[55],"certain":[56],"assumptions.":[57],"Numerical":[58],"results":[59],"are":[60],"given":[61],"verify":[63],"efficiency":[65],"of":[66],"method.":[69]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}