{"id":"https://openalex.org/W2080058947","doi":"https://doi.org/10.1080/00207160.2015.1045420","title":"The right\u2013left preconditioning technique for the solution of the large matrix equation<i>AXB = C</i>","display_name":"The right\u2013left preconditioning technique for the solution of the large matrix equation<i>AXB = C</i>","publication_year":2015,"publication_date":"2015-04-28","ids":{"openalex":"https://openalex.org/W2080058947","doi":"https://doi.org/10.1080/00207160.2015.1045420","mag":"2080058947"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1045420","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1045420","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5101420765","display_name":"Saeed Karimi","orcid":"https://orcid.org/0009-0001-8596-5068"},"institutions":[{"id":"https://openalex.org/I90767664","display_name":"Persian Gulf University","ror":"https://ror.org/03n2mgj60","country_code":"IR","type":"education","lineage":["https://openalex.org/I90767664"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Saeed Karimi","raw_affiliation_strings":["Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran","Department of Mathematics, Persian Gulf University, Bushehr75169, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran","institution_ids":["https://openalex.org/I90767664"]},{"raw_affiliation_string":"Department of Mathematics, Persian Gulf University, Bushehr75169, Iran#TAB#","institution_ids":["https://openalex.org/I90767664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101420765"],"corresponding_institution_ids":["https://openalex.org/I90767664"],"apc_list":null,"apc_paid":null,"fwci":0.3505,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.64393041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"93","issue":"7","first_page":"1226","last_page":"1239"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9818000197410583,"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/mathematics","display_name":"Mathematics","score":0.873002290725708},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.7744842767715454},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7330582737922668},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6457246541976929},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.584516704082489},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5405892133712769},{"id":"https://openalex.org/keywords/matrix-difference-equation","display_name":"Matrix difference equation","score":0.4599122107028961},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.43287140130996704},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.42953920364379883},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42591580748558044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.388294517993927},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.35514673590660095},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.25841957330703735},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22678682208061218},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.19360938668251038},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.07338923215866089},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.06723755598068237}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.873002290725708},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.7744842767715454},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7330582737922668},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6457246541976929},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.584516704082489},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5405892133712769},{"id":"https://openalex.org/C47285271","wikidata":"https://www.wikidata.org/wiki/Q6787869","display_name":"Matrix difference equation","level":4,"score":0.4599122107028961},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.43287140130996704},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.42953920364379883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42591580748558044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.388294517993927},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.35514673590660095},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.25841957330703735},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22678682208061218},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.19360938668251038},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.07338923215866089},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.06723755598068237},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1045420","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1045420","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W185873980","https://openalex.org/W1580973103","https://openalex.org/W1971734187","https://openalex.org/W1992752360","https://openalex.org/W2005691328","https://openalex.org/W2023686904","https://openalex.org/W2047156571","https://openalex.org/W2054743364","https://openalex.org/W2055000341","https://openalex.org/W2060487795","https://openalex.org/W2066021453","https://openalex.org/W2079891271","https://openalex.org/W2081128548","https://openalex.org/W2085940840","https://openalex.org/W2097897435","https://openalex.org/W2160835412","https://openalex.org/W2168947999","https://openalex.org/W3140368695","https://openalex.org/W4206263661","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W2201410197","https://openalex.org/W4381661905","https://openalex.org/W4308005071","https://openalex.org/W27112594","https://openalex.org/W2372553422","https://openalex.org/W2079117061","https://openalex.org/W2388544145","https://openalex.org/W2007703035","https://openalex.org/W2806418911","https://openalex.org/W2371373832"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper,":[2],"the":[3,36,55,59,68,80,91,110,113],"linear":[4],"matrix":[5,42,61],"equation":[6],"AXB=C":[7],"is":[8,32,51,65,73],"considered,":[9],"where":[10,71],"A\u2208Rn\u00d7m,":[11],"B\u2208Rq\u00d7s":[12],"are":[13,20,87,106],"given":[14,107],"large":[15],"matrices":[16,98],"and":[17,23,83,99],"C\u2208Rn\u00d7s,":[18],"X\u2208Rm\u00d7q":[19],"right-hand":[21],"side":[22],"unknown":[24],"matrices,":[25],"respectively.":[26],"The":[27,44],"global":[28,47],"least":[29,48],"squares":[30,49],"algorithm":[31,50,86],"applied":[33],"to":[34,89,108],"approximate":[35,56,92],"solution":[37,57],"of":[38,41,58,95,112],"group":[40],"equations.":[43],"right\u2013left":[45],"preconditioned":[46,85],"presented":[52],"for":[53],"obtaining":[54],"mentioned":[60],"equation.":[62],"This":[63],"preconditioner":[64],"based":[66],"on":[67],"C-orthogonalization":[69],"process,":[70],"C":[72],"a":[74],"symmetric":[75],"positive":[76],"definite":[77],"matrix.":[78],"Also,":[79],"iterative":[81],"method":[82],"its":[84],"proposed":[88],"find":[90],"generalized":[93],"inverses":[94],"nearly":[96],"singular":[97],"rectangular":[100],"matrices.":[101],"Finally,":[102],"some":[103],"numerical":[104],"experiments":[105],"illustrate":[109],"efficiency":[111],"new":[114],"preconditioners.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
