{"id":"https://openalex.org/W1980249685","doi":"https://doi.org/10.1016/s0024-3795(02)00471-8","title":"Inversion of two level circulant matrices over Zp","display_name":"Inversion of two level circulant matrices over Zp","publication_year":2003,"publication_date":"2003-04-23","ids":{"openalex":"https://openalex.org/W1980249685","doi":"https://doi.org/10.1016/s0024-3795(02)00471-8","mag":"1980249685"},"language":"en","primary_location":{"id":"doi:10.1016/s0024-3795(02)00471-8","doi":"https://doi.org/10.1016/s0024-3795(02)00471-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0024-3795(02)00471-8","pdf_url":null,"source":{"id":"https://openalex.org/S159544283","display_name":"Linear Algebra and its Applications","issn_l":"0024-3795","issn":["0024-3795","1873-1856"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Linear Algebra and its Applications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.1016/s0024-3795(02)00471-8","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018418920","display_name":"Carlo J. Accettella","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo J. Accettella","raw_affiliation_strings":["Dipartimento di Informatic\u00e0, Universit\u00e0 di Pisa, 56100 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatic\u00e0, Universit\u00e0 di Pisa, 56100 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044619255","display_name":"Gianna M. Del Corso","orcid":"https://orcid.org/0000-0002-5651-9368","observed_orcids":["https://orcid.org/0000-0002-5651-9368"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianna M. Del Corso","raw_affiliation_strings":["Dipartimento di Informatic\u00e0, Universit\u00e0 di Pisa, 56100 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatic\u00e0, Universit\u00e0 di Pisa, 56100 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049381844","display_name":"Giovanni Manzini","orcid":"https://orcid.org/0000-0002-5047-0196","observed_orcids":["https://orcid.org/0000-0002-5047-0196"]},"institutions":[{"id":"https://openalex.org/I4210130157","display_name":"Institute of Informatics and Telematics","ror":"https://ror.org/02gdcn153","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210130157","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Manzini","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 del Piemonte Orientale, Alessandria, and IIT-CNR, Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 del Piemonte Orientale, Alessandria, and IIT-CNR, Pisa, Italy","institution_ids":["https://openalex.org/I4210130157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3230,"currency":"USD","value_usd":3230},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.1163227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"366","issue":null,"first_page":"5","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9560999870300293,"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":0.9560999870300293,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.006000000052154064,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.005200000014156103,"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/matrix-inversion","display_name":"matrix inversion","score":0.8410000205039978},{"id":"https://openalex.org/keywords/circulant-matrices","display_name":"circulant matrices","score":0.8980000019073486},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.6359999775886536},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.5120000243186951}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.9590601921081543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8341021537780762},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6340256333351135},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5883991122245789},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5218048095703125},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5125072002410889},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4333970844745636},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4259997606277466},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.41535013914108276},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.41135817766189575},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3684425354003906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.194821298122406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11691209673881531},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09924298524856567},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1016/s0024-3795(02)00471-8","doi":"https://doi.org/10.1016/s0024-3795(02)00471-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0024-3795(02)00471-8","pdf_url":null,"source":{"id":"https://openalex.org/S159544283","display_name":"Linear Algebra and its Applications","issn_l":"0024-3795","issn":["0024-3795","1873-1856"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Linear Algebra and its Applications","raw_type":"journal-article"},{"id":"pmh:oai:eprints.adm.unipi.it:2062","doi":null,"is_oa":false,"landing_page_url":"http://eprints.adm.unipi.it/2062/1/TR%2D01%2D17.ps.gz","pdf_url":null,"source":{"id":"https://openalex.org/S4306401711","display_name":"UnipiEprints Open Archive (Universit\u00e0 di Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Book"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.4229","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.4229","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.di.unipi.it/pub/techreports/TR-01-17.ps.Z","raw_type":"text"},{"id":"pmh:oai:arpi.unipi.it:11568/76898","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/76898","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pumaoai.isti.cnr.it:cnr.iit/cnr.iit/2003-A0-016","doi":null,"is_oa":true,"landing_page_url":"http://puma.isti.cnr.it/dfdownloadnew.php?ident=cnr.iit/cnr.iit/2003-A0-016","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"In: LINEAR ALGEBRA AND ITS APPLICATIONS (65219J0), vol. 366 pp. 5 - 23. Science Direc t, 2003.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1016/s0024-3795(02)00471-8","doi":"https://doi.org/10.1016/s0024-3795(02)00471-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0024-3795(02)00471-8","pdf_url":null,"source":{"id":"https://openalex.org/S159544283","display_name":"Linear Algebra and its Applications","issn_l":"0024-3795","issn":["0024-3795","1873-1856"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Linear Algebra and its Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W208025404","https://openalex.org/W1532046361","https://openalex.org/W1562183207","https://openalex.org/W1568760617","https://openalex.org/W1763997349","https://openalex.org/W2047837169","https://openalex.org/W2059732659","https://openalex.org/W2089900710","https://openalex.org/W2110958644"],"related_works":["https://openalex.org/W7095805008","https://openalex.org/W1763997349","https://openalex.org/W1805753725","https://openalex.org/W2742943992","https://openalex.org/W2365997553","https://openalex.org/W2356721246","https://openalex.org/W2113477837","https://openalex.org/W2357168079","https://openalex.org/W3146545874","https://openalex.org/W4392678146"],"abstract_inverted_index":{"We":[0,71],"consider":[1],"the":[2,16,23,32,57],"problem":[3,20,52,59],"of":[4,25,26,40,60,77],"inverting":[5,61],"block":[6],"circulant":[7,9,63],"with":[8,13,65],"blocks":[10],"BCCB":[11,75],"matrices":[12],"entries":[14,66],"over":[15,47,67],"field":[17],"$Zp$.":[18],"This":[19],"arises":[21],"in":[22,83,88,97],"study":[24],"two-dimensional":[27],"linear":[28],"cellular":[29],"automata.":[30],"Since":[31],"standard":[33],"reduction":[34],"to":[35],"diagonal":[36],"form":[37],"by":[38,53],"means":[39],"FFT":[41],"has":[42],"some":[43],"drawbacks":[44],"when":[45],"working":[46],"$Zp$,":[48,89],"we":[49],"solve":[50],"this":[51],"transforming":[54],"it":[55],"into":[56],"equivalent":[58],"a":[62,68,74,93],"matrix":[64,76],"suitable":[69],"ring~$R$.":[70],"show":[72],"that":[73],"size":[78],"$mn$":[79],"can":[80],"be":[81],"inverted":[82],"$O{m":[84],"n,":[85],"c(m,n)}$":[86],"operations":[87],"where":[90],"$c$":[91],"is":[92],"low":[94],"degree":[95],"polynomial":[96],"$log":[98,101],"m$":[99],"and":[100],"n$.":[102]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
