{"id":"https://openalex.org/W3195170616","doi":"https://doi.org/10.1137/20m1379666","title":"The Asymptotic Spectrum of Flipped Multilevel Toeplitz Matrices and of Certain Preconditionings","display_name":"The Asymptotic Spectrum of Flipped Multilevel Toeplitz Matrices and of Certain Preconditionings","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3195170616","doi":"https://doi.org/10.1137/20m1379666","mag":"3195170616"},"language":"en","primary_location":{"id":"doi:10.1137/20m1379666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379666","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5022749162","display_name":"Mariarosa Mazza","orcid":"https://orcid.org/0000-0002-8505-6788"},"institutions":[{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. Mazza","raw_affiliation_strings":["Department of Humanities and Innovation, University of Insubria, via Valleggio 11, 22100 Como, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8505-6788","affiliations":[{"raw_affiliation_string":"Department of Humanities and Innovation, University of Insubria, via Valleggio 11, 22100 Como, Italy","institution_ids":["https://openalex.org/I115752224"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062815653","display_name":"Jennifer Pestana","orcid":"https://orcid.org/0000-0003-1527-3178"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. Pestana","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Strathclyde, 16 Richmond Street, Glasgow G1 1XQ, UK"],"raw_orcid":"https://orcid.org/0000-0003-1527-3178","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Strathclyde, 16 Richmond Street, Glasgow G1 1XQ, UK","institution_ids":["https://openalex.org/I181647926"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6089,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.72712018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"3","first_page":"1319","last_page":"1336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9860954284667969},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.840752363204956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8181616067886353},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.7217313051223755},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6469687819480896},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5355736017227173},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5044623613357544},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5034932494163513},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4525456130504608},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3148825764656067},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06391283869743347}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9860954284667969},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.840752363204956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8181616067886353},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.7217313051223755},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6469687819480896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5355736017227173},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5044623613357544},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5034932494163513},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4525456130504608},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3148825764656067},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06391283869743347},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1379666","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379666","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:art.torvergata.it:2108/344024","is_oa":false,"landing_page_url":"https://hdl.handle.net/2108/344024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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:irinsubria.uninsubria.it:11383/2120653","is_oa":false,"landing_page_url":"http://hdl.handle.net/11383/2120653","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/2142133","is_oa":false,"landing_page_url":"https://hdl.handle.net/11383/2142133","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4361165789","display_name":null,"funder_award_id":"EP/R009821/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8166419689","display_name":"Effective preconditioners for linear systems in fractional diffusion","funder_award_id":"EP/R009821/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1504178724","https://openalex.org/W1969578814","https://openalex.org/W1980058119","https://openalex.org/W2001011967","https://openalex.org/W2004386400","https://openalex.org/W2017732348","https://openalex.org/W2034324318","https://openalex.org/W2078692435","https://openalex.org/W2103603805","https://openalex.org/W2685992850","https://openalex.org/W2789730805","https://openalex.org/W2882989027","https://openalex.org/W2903335383","https://openalex.org/W2957570416","https://openalex.org/W2972868794","https://openalex.org/W3033387009","https://openalex.org/W3163076066"],"related_works":["https://openalex.org/W2286689764","https://openalex.org/W4220662591","https://openalex.org/W2051015700","https://openalex.org/W2091997962","https://openalex.org/W2203419549","https://openalex.org/W2364268279","https://openalex.org/W2105266774","https://openalex.org/W2391178808","https://openalex.org/W4243833160","https://openalex.org/W2034324318"],"abstract_inverted_index":{"In":[0,52],"this":[1],"work,":[2],"we":[3,14,56,83],"perform":[4],"a":[5,27,35,71],"spectral":[6,18],"analysis":[7,97],"of":[8,20,88],"flipped":[9,61,91],"multilevel":[10,30,92,101],"Toeplitz":[11,31,62,93,102],"sequences,":[12,64],"i.e.,":[13],"study":[15],"the":[16,42,49,65,85],"asymptotic":[17,66],"behavior":[19],"$\\{Y_{{n}}":[21],"T_{{n}}":[22],"(f)\\}_{{n}}$,":[23],"where":[24],"$T_{{n}}(f)$":[25],"is":[26,41,68],"real,":[28],"square":[29],"matrix":[32,63],"generated":[33],"by":[34,70,112],"function":[36,76],"$f\\in":[37],"L^1([-\\pi,\\pi]^d)$":[38],"and":[39,103],"$Y_n$":[40],"exchange":[43],"matrix,":[44],"which":[45],"has":[46],"1's":[47],"on":[48],"main":[50],"antidiagonal.":[51],"line":[53],"with":[54,95],"what":[55],"have":[57],"shown":[58],"for":[59],"unilevel":[60],"spectrum":[67],"determined":[69],"2":[72,74],"x":[73],"matrix-valued":[75],"whose":[77],"eigenvalues":[78],"are":[79,110],"$\\pm":[80],"|f|$.":[81],"Furthermore,":[82],"characterize":[84],"eigenvalue":[86],"distribution":[87],"certain":[89],"preconditioned":[90],"sequences":[94],"an":[96],"that":[98],"covers":[99],"both":[100],"circulant":[104],"preconditioners.":[105],"Finally,":[106],"all":[107],"our":[108],"findings":[109],"illustrated":[111],"several":[113],"numerical":[114],"experiments.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
