{"id":"https://openalex.org/W4389518611","doi":"https://doi.org/10.32523/2306-6172-2023-11-4-130-142","title":"TWO ALGEBRAIC ALGORITHMS FOR THE LU DECOMPOSITION OF COMMUTATIVE QUATERNION MATRICES AND THEIR APPLICATIONS","display_name":"TWO ALGEBRAIC ALGORITHMS FOR THE LU DECOMPOSITION OF COMMUTATIVE QUATERNION MATRICES AND THEIR APPLICATIONS","publication_year":2023,"publication_date":"2023-12-01","ids":{"openalex":"https://openalex.org/W4389518611","doi":"https://doi.org/10.32523/2306-6172-2023-11-4-130-142"},"language":"en","primary_location":{"id":"doi:10.32523/2306-6172-2023-11-4-130-142","doi":"https://doi.org/10.32523/2306-6172-2023-11-4-130-142","is_oa":false,"landing_page_url":"http://dx.doi.org/10.32523/2306-6172-2023-11-4-130-142","pdf_url":null,"source":{"id":"https://openalex.org/S4210169599","display_name":"Eurasian Journal of Mathematical and Computer Applications","issn_l":"2306-6172","issn":["2306-6172","2308-9822"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","jufo-1","poland-40","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Eurasian Journal of Mathematical and Computer Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5056103860","display_name":"Dong Zhang","orcid":"https://orcid.org/0000-0003-4688-7762","observed_orcids":["https://orcid.org/0000-0003-4688-7762"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dong Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5056103860"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"4","first_page":"130","last_page":"142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.6182000041007996,"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":0.6182000041007996,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.35499998927116394,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.004000000189989805,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.9890000224113464},{"id":"https://openalex.org/keywords/algebraic-algorithms","display_name":"algebraic algorithms","score":0.796999990940094},{"id":"https://openalex.org/keywords/structure-preserving-algorithms","display_name":"structure-preserving algorithms","score":0.8109999895095825},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.9010000228881836},{"id":"https://openalex.org/keywords/color-image-restoration","display_name":"color image restoration","score":0.9950000047683716}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9053951501846313},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.6926819682121277},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6092469692230225},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5791875123977661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5086987614631653},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5012562274932861},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4631001651287079},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4586811363697052},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4426094591617584},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.43643954396247864},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.42352765798568726},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.415168821811676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3421659469604492},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3223959803581238},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15956008434295654},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1509542167186737},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.32523/2306-6172-2023-11-4-130-142","doi":"https://doi.org/10.32523/2306-6172-2023-11-4-130-142","is_oa":false,"landing_page_url":"http://dx.doi.org/10.32523/2306-6172-2023-11-4-130-142","pdf_url":null,"source":{"id":"https://openalex.org/S4210169599","display_name":"Eurasian Journal of Mathematical and Computer Applications","issn_l":"2306-6172","issn":["2306-6172","2308-9822"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","jufo-1","poland-40","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Eurasian Journal of Mathematical and Computer Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391188028","https://openalex.org/W7157574836","https://openalex.org/W4406662884","https://openalex.org/W4280654432","https://openalex.org/W1973310238","https://openalex.org/W4413067410","https://openalex.org/W4399565968","https://openalex.org/W4283808690","https://openalex.org/W4387669484","https://openalex.org/W4382749345"],"abstract_inverted_index":{"The":[0,15,62],"paper":[1,63],"proposes":[2],"two":[3],"algebraic":[4,21],"algorithms":[5],"for":[6,75],"the":[7,30,52,66,80,85,89],"LU":[8,53],"decomposition":[9,54],"of":[10,17,41,55,68,71,88],"com-":[11],"mutative":[12],"quaternion":[13,43,57],"matrices.":[14,44],"first":[16,90],"them":[18],"is":[19,32,59],"an":[20],"algorithm":[22,36],"based":[23,37],"on":[24,38],"a":[25,33,72],"complex":[26,34],"representation":[27],"matrix,":[28],"and":[29],"second":[31],"structure-preserving":[35],"Gaussian":[39],"elimination":[40],"commutative":[42,56],"With":[45],"their":[46],"help,":[47],"it":[48],"was":[49],"established":[50],"that":[51],"matrices":[58],"not":[60],"unique.":[61],"also":[64],"presents":[65],"results":[67],"numerical":[69],"implementations":[70],"mathematical":[73],"model":[74],"color":[76],"image":[77],"restoration":[78],"using":[79],"proposed":[81],"algorithms,":[82],"which":[83],"demonstrated":[84],"higher":[86],"efficiency":[87],"algorithm.":[91]},"counts_by_year":[],"updated_date":"2026-09-11T09:22:31.653822","created_date":"2023-12-10T00:00:00"}
