{"id":"https://openalex.org/W1988976163","doi":"https://doi.org/10.1137/s0895479896310160","title":"Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices","display_name":"Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1988976163","doi":"https://doi.org/10.1137/s0895479896310160","mag":"1988976163"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479896310160","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896310160","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/A5053268193","display_name":"Stefano Serra\u2010Capizzano","orcid":"https://orcid.org/0000-0001-9477-109X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stefano Serra","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053268193"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3808,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.97070707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"1","first_page":"31","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9883000254631042,"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":0.9318112134933472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7792645692825317},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6431357860565186},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5433093309402466},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5115736126899719},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49483364820480347},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45122969150543213},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4162341356277466},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3529770076274872},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32491111755371094},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07520762085914612}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9318112134933472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7792645692825317},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6431357860565186},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5433093309402466},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5115736126899719},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49483364820480347},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45122969150543213},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4162341356277466},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3529770076274872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32491111755371094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07520762085914612},{"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":1,"locations":[{"id":"doi:10.1137/s0895479896310160","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896310160","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1594563152","https://openalex.org/W1763997349","https://openalex.org/W1970334228","https://openalex.org/W1975696503","https://openalex.org/W1976865075","https://openalex.org/W1988177606","https://openalex.org/W1994176509","https://openalex.org/W1995772663","https://openalex.org/W1997992827","https://openalex.org/W2003977554","https://openalex.org/W2005041367","https://openalex.org/W2008723004","https://openalex.org/W2014835357","https://openalex.org/W2018468554","https://openalex.org/W2043909302","https://openalex.org/W2044905083","https://openalex.org/W2045463928","https://openalex.org/W2047151498","https://openalex.org/W2049847986","https://openalex.org/W2057439610","https://openalex.org/W2058478885","https://openalex.org/W2064616889","https://openalex.org/W2066750794","https://openalex.org/W2072820862","https://openalex.org/W2080097309","https://openalex.org/W2082830265","https://openalex.org/W2089598668","https://openalex.org/W2092085096","https://openalex.org/W2116496516","https://openalex.org/W2134572726","https://openalex.org/W2138152282","https://openalex.org/W2169487141","https://openalex.org/W2326028551","https://openalex.org/W2726555835","https://openalex.org/W2798909945","https://openalex.org/W3026026050","https://openalex.org/W4239165712","https://openalex.org/W4252589316","https://openalex.org/W4256076666","https://openalex.org/W4285719527","https://openalex.org/W4301085805"],"related_works":["https://openalex.org/W2081990255","https://openalex.org/W110533479","https://openalex.org/W4248194227","https://openalex.org/W2047814828","https://openalex.org/W4213072858","https://openalex.org/W1998860845","https://openalex.org/W4313640449","https://openalex.org/W3183252893","https://openalex.org/W4361002216","https://openalex.org/W1977278511"],"abstract_inverted_index":{"It":[0],"is":[1],"well":[2,162],"known":[3],"that":[4,120],"the":[5,23,29,90,124,165],"generating":[6,78],"function":[7,79],"$f\\in":[8,80],"L^1([-\\pi,\\pi],{\\tiny":[9,81],"{\\bf":[10,82],"R}})$":[11],"of":[12,15,25,28,93,215],"a":[13,75],"class":[14],"Hermitian":[16,76],"Toeplitz":[17,36,66,126,167,199],"matrices":[18,67,200],"An(f)":[19],"describes":[20],"very":[21],"precisely":[22],"spectrum":[24],"each":[26],"matrix":[27],"class.":[30],"[U.":[31],"Grenader":[32],"and":[33,38,103,133,191,203,219],"G.":[34,131],"Szeg\u00f6,":[35],"Forms":[37],"Their":[39,220],"Applications,":[40,221],"2nd":[41],"ed.,":[42],"Chelsea,":[43],"New":[44,223],"York,":[45,224],"1984;":[46],"E.":[47,48,226],"Tyrtyshnikov,":[49],"Linear":[50,171],"Algebra":[51,172],"Appl.,":[52,110,138,149,173],"232":[53],"(1996),":[54,151],"pp.":[55,141,152,159,176],"1--43].":[56],"In":[57],"this":[58,99,118],"paper":[59],"we":[60,88,113],"consider":[61],"n":[62,64],"\u00d7":[63,70],"block":[65],"with":[68,184],"m":[69,71],"blocks":[72],"generated":[73],"by":[74],"matrix-valued":[77],"C}}^{m\\times":[83],"m})$":[84],"and,":[85],"in":[86,123,164,201],"particular,":[87],"analyze":[89],"associated":[91],"problem":[92],"preconditioning.":[94],"Using":[95],"previous":[96],"results":[97],"on":[98,198],"topic":[100],"[P.":[101],"Tilli":[102],"M.":[104,210],"Miranda,":[105],"SIAM":[106,145],"J.":[107,146],"Matrix":[108,147],"Anal.":[109,148],"to":[111,117,229],"appear],":[112],"extend":[114],"some":[115],"theorems":[116],"case":[119,127,168],"were":[121],"proved":[122],"one-level":[125],"[F.":[128],"Di":[129],"Benedetto,":[130],"Fiorentino,":[132],"S.":[134,143,154],"Serra,":[135,144,155,170],"Comput.":[136],"Math.":[137],"25":[139],"(1993),":[140],"35--45;":[142],"17":[150],"1007--1019;":[153],"Calcolo,":[156],"32":[157],"(1995),":[158],"153--176]":[160],"as":[161,163],"two-level":[166],"[S.":[169],"270":[174],"(1998),":[175],"109--129].":[177],"This":[178],"idea":[179],"seems":[180],"promising":[181],"when":[182],"dealing":[183],"linear":[185],"systems":[186],"arising":[187],"from":[188],"control":[189],"theory":[190,194],"Markov":[192],"chains":[193],"[R.":[195],"Preuss,":[196],"Workshop":[197],"Filtering":[202],"Control,":[204],"Santa":[205],"Barbara,":[206],"CA,":[207],"August":[208],"1996;":[209],"Neuts,":[211],"Structured":[212],"Stochastic":[213,230],"Matrices":[214],"M/G/":[216],"1":[217],"Type":[218],"Dekker,":[222],"1989;":[225],"Cinlar,":[227],"Introduction":[228],"Processes,":[231],"Prentice--Hall,":[232],"Englewood":[233],"Cliffs,":[234],"NJ,":[235],"1975].":[236]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}