{"id":"https://openalex.org/W3099694885","doi":"https://doi.org/10.3390/info11110523","title":"A Method of Ultra-Large-Scale Matrix Inversion Using Block Recursion","display_name":"A Method of Ultra-Large-Scale Matrix Inversion Using Block Recursion","publication_year":2020,"publication_date":"2020-11-10","ids":{"openalex":"https://openalex.org/W3099694885","doi":"https://doi.org/10.3390/info11110523","mag":"3099694885"},"language":"en","primary_location":{"id":"doi:10.3390/info11110523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11110523","pdf_url":"https://www.mdpi.com/2078-2489/11/11/523/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2078-2489/11/11/523/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068117437","display_name":"Houzhen Wang","orcid":"https://orcid.org/0000-0003-2773-5050"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"HouZhen Wang","raw_affiliation_strings":["Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100614809","display_name":"Yan Guo","orcid":"https://orcid.org/0000-0002-5987-201X"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Guo","raw_affiliation_strings":["Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026793623","display_name":"Huanguo Zhang","orcid":"https://orcid.org/0000-0001-5801-2897"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"HuanGuo Zhang","raw_affiliation_strings":["Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068117437"],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.6172,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83914053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"11","issue":"11","first_page":"523","last_page":"523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.8144484758377075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.669894814491272},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6567474603652954},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5554846525192261},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5348540544509888},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.5287781953811646},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.497670441865921},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4671131372451782},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.464228093624115},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.455024778842926},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4492373764514923},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4469911456108093},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4021245241165161},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37664127349853516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2158752679824829}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.8144484758377075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.669894814491272},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6567474603652954},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5554846525192261},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5348540544509888},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.5287781953811646},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.497670441865921},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4671131372451782},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.464228093624115},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.455024778842926},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4492373764514923},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4469911456108093},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4021245241165161},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37664127349853516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2158752679824829},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/info11110523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11110523","pdf_url":"https://www.mdpi.com/2078-2489/11/11/523/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:94850868ff874146ada5c7b7ac46bc8a","is_oa":true,"landing_page_url":"https://doaj.org/article/94850868ff874146ada5c7b7ac46bc8a","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":"Information, Vol 11, Iss 11, p 523 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2078-2489/11/11/523/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/info11110523","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information; Volume 11; Issue 11; Pages: 523","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/info11110523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11110523","pdf_url":"https://www.mdpi.com/2078-2489/11/11/523/pdf","source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3099694885.pdf","grobid_xml":"https://content.openalex.org/works/W3099694885.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W29048791","https://openalex.org/W1558108883","https://openalex.org/W1972332180","https://openalex.org/W1976641808","https://openalex.org/W1994840943","https://openalex.org/W2009871859","https://openalex.org/W2035476608","https://openalex.org/W2060669094","https://openalex.org/W2138791376","https://openalex.org/W2150365180","https://openalex.org/W2164489987","https://openalex.org/W2165928982","https://openalex.org/W2315072896","https://openalex.org/W2963451778","https://openalex.org/W4205986662"],"related_works":["https://openalex.org/W1970548269","https://openalex.org/W2165928982","https://openalex.org/W3091817928","https://openalex.org/W3136257861","https://openalex.org/W1543798151","https://openalex.org/W4226309051","https://openalex.org/W2786640160","https://openalex.org/W2132877936","https://openalex.org/W2280540821","https://openalex.org/W3099694885"],"abstract_inverted_index":{"Ultra-large-scale":[0],"matrix":[1,21],"inversion":[2],"has":[3,59],"been":[4],"applied":[5],"as":[6,25,51],"the":[7,15,28,57,89,95,102,105],"fundamental":[8],"operation":[9],"of":[10,17,30,46,107],"numerous":[11],"domains,":[12],"owing":[13],"to":[14,114],"growth":[16],"big":[18],"data":[19],"and":[20,104],"applications.":[22],"Using":[23,110],"cryptography":[24],"an":[26],"example,":[27],"solution":[29],"ultra-large-scale":[31],"linear":[32],"equations":[33],"over":[34],"finite":[35],"fields":[36],"is":[37,54],"important":[38],"in":[39,52,120],"many":[40],"cryptanalysis":[41],"schemes.":[42],"However,":[43],"inverting":[44],"matrices":[45,76],"extremely":[47],"high":[48],"order,":[49],"such":[50],"millions,":[53],"challenging;":[55],"nonetheless,":[56],"need":[58],"become":[60],"increasingly":[61],"urgent.":[62],"Hence,":[63],"we":[64,87],"propose":[65],"a":[66,78,121],"parallel":[67],"distributed":[68],"block":[69],"recursive":[70],"computing":[71],"method":[72],"that":[73],"can":[74,117],"process":[75],"at":[77],"significantly":[79],"increased":[80],"scale,":[81],"based":[82,98],"on":[83,99],"Strassen\u2019s":[84],"method;":[85],"furthermore,":[86],"describe":[88],"related":[90],"well-designed":[91],"algorithm":[92],"herein.":[93],"Additionally,":[94],"experimental":[96],"results":[97],"comparison":[100],"show":[101],"efficiency":[103],"superiority":[106],"our":[108,111],"method.":[109],"method,":[112],"up":[113],"140,000":[115],"dimensions":[116],"be":[118],"processed":[119],"supercomputing":[122],"center.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}