{"id":"https://openalex.org/W2554229472","doi":"https://doi.org/10.1090/mcom/3301","title":"Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes","display_name":"Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes","publication_year":2017,"publication_date":"2017-06-29","ids":{"openalex":"https://openalex.org/W2554229472","doi":"https://doi.org/10.1090/mcom/3301","mag":"2554229472"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3301","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3301","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.06337","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023356208","display_name":"Dario A. Bini","orcid":"https://orcid.org/0000-0002-5885-9411"},"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"]},{"id":"https://openalex.org/I4210160382","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Pisa","ror":"https://ror.org/05symbg58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210160382"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dario Bini","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00c3\u00a0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","Dipartimento di Matematica, Universit\u00e0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00c3\u00a0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I4210160382","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030708699","display_name":"Stefano Massei","orcid":"https://orcid.org/0000-0003-1813-4181"},"institutions":[{"id":"https://openalex.org/I157210198","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10","country_code":"IT","type":"education","lineage":["https://openalex.org/I157210198"]},{"id":"https://openalex.org/I4210122060","display_name":"Mathys (Switzerland)","ror":"https://ror.org/02skjv125","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210122060"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","IT"],"is_corresponding":false,"raw_author_name":"Stefano Massei","raw_affiliation_strings":["EPFL SB MATH ANCHP, CH-1015 Lausanne, Switzerland","Scuola Normale Superiore, Cavalieri 7, 56126 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EPFL SB MATH ANCHP, CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I4210122060","https://openalex.org/I5124864"]},{"raw_affiliation_string":"Scuola Normale Superiore, Cavalieri 7, 56126 Pisa, Italy","institution_ids":["https://openalex.org/I157210198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000363133","display_name":"Beatrice Meini","orcid":"https://orcid.org/0000-0003-3139-2513"},"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"]},{"id":"https://openalex.org/I4210160382","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Pisa","ror":"https://ror.org/05symbg58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210160382"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Beatrice Meini","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00c3\u00a0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","Dipartimento di Matematica, Universit\u00e0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00c3\u00a0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I4210160382","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Pisa, Largo B Pontecorvo 5, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7498,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.91108899,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"87","issue":"314","first_page":"2811","last_page":"2830"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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/T11716","display_name":"Random Matrices and Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9979000091552734,"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/mathematics","display_name":"Mathematics","score":0.7714003324508667},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7165395021438599},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5943445563316345},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.580443799495697},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.513526976108551},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.5081312656402588},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4939876198768616},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41960638761520386},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32284635305404663},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2423647940158844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14971092343330383},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09857833385467529}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7714003324508667},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7165395021438599},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5943445563316345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.580443799495697},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.513526976108551},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5081312656402588},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4939876198768616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41960638761520386},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32284635305404663},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2423647940158844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14971092343330383},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09857833385467529},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/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:10.1090/mcom/3301","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3301","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.06337","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1611.06337","pdf_url":"https://arxiv.org/pdf/1611.06337","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:arpi.unipi.it:11568/886963","is_oa":false,"landing_page_url":"http://www.ams.org/journals/mcom/2018-87-314/S0025-5718-2018-03301-4/","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,"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:infoscience.epfl.ch:259915","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/150936","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.06337","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1611.06337","pdf_url":"https://arxiv.org/pdf/1611.06337","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W642183039","https://openalex.org/W1483073639","https://openalex.org/W1498989325","https://openalex.org/W1517350773","https://openalex.org/W1550150926","https://openalex.org/W1577300772","https://openalex.org/W1942047793","https://openalex.org/W1968661925","https://openalex.org/W1990523337","https://openalex.org/W1990820401","https://openalex.org/W2002343677","https://openalex.org/W2003412314","https://openalex.org/W2006084938","https://openalex.org/W2006850990","https://openalex.org/W2019185649","https://openalex.org/W2020928982","https://openalex.org/W2045712380","https://openalex.org/W2045933510","https://openalex.org/W2060259097","https://openalex.org/W2062573385","https://openalex.org/W2069419970","https://openalex.org/W2077095314","https://openalex.org/W2080497978","https://openalex.org/W2086391916","https://openalex.org/W2089598668","https://openalex.org/W2103457383","https://openalex.org/W2107330716","https://openalex.org/W2110958644","https://openalex.org/W2112457757","https://openalex.org/W2154602821","https://openalex.org/W2511513462","https://openalex.org/W2528577254","https://openalex.org/W2554313615","https://openalex.org/W2555789848","https://openalex.org/W2571023458","https://openalex.org/W2765527408","https://openalex.org/W2899496263","https://openalex.org/W2950472576","https://openalex.org/W2962979508","https://openalex.org/W2970256618","https://openalex.org/W4240681401","https://openalex.org/W4244639301","https://openalex.org/W4248635868","https://openalex.org/W4250179369","https://openalex.org/W4285719527","https://openalex.org/W4300046645","https://openalex.org/W4302998288"],"related_works":["https://openalex.org/W4288083145","https://openalex.org/W2905007567","https://openalex.org/W4289116096","https://openalex.org/W4280509587","https://openalex.org/W4377989614","https://openalex.org/W1490256933","https://openalex.org/W1604903594","https://openalex.org/W2951683022","https://openalex.org/W4291238690","https://openalex.org/W2131680714"],"abstract_inverted_index":{"Denote":[0],"by":[1],"<inline-formula":[2,35,116,205,223,268,303],"content-type=\"math/mathml\">":[3,36,117,206,224,269,304],"<mml:math":[4,37,118,207,225,270,305],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,38,119,208,226,271,306],"alttext=\"script":[6],"upper":[7,233,275,281,327],"W":[8,234],"1\">":[9,235],"<mml:semantics>":[10,63,142,211,236,283,332],"<mml:msub>":[11,97,175,247,343,352],"<mml:mrow":[12,76,88,148,160,169,179,248,345],"class=\"MJX-TeXAtom-ORD\">":[13,77,89,149,161,170,180,249,346],"<mml:mi":[14,83,91,155,163,185,250],"class=\"MJX-tex-caligraphic\"":[15,251],"mathvariant=\"script\">W</mml:mi>":[16,252],"</mml:mrow>":[17,87,95,105,159,167,173,183,189,253,256,295,350],"<mml:mn>1</mml:mn>":[18,254],"</mml:msub>":[19,100,178,255,351],"<mml:annotation":[20,106,190,213,257,296],"encoding=\"application/x-tex\">\\mathcal":[21],"{W}_1</mml:annotation>":[22],"</mml:semantics>":[23,111,195,215,261,298],"</mml:math>":[24,112,196,216,262,299],"</inline-formula>":[25,113,197,217,263,300],"the":[26,33,266],"set":[27],"of":[28,32,265],"complex":[29],"valued":[30],"functions":[31],"form":[34,267],"alttext=\"a":[39,227],"left-parenthesis":[40,228,277,309,313],"z":[41,60,229],"right-parenthesis":[42,230,279,311,320],"equals":[43,47,123,274,312],"sigma-summation":[44],"Underscript":[45,121],"i":[46,58,122,133,136,316,322],"negative":[48,124],"normal":[49,53,125,129,140],"infinity":[50,54,126,130],"Overscript":[51,127],"plus":[52,128,280],"Endscripts":[55,131],"a":[56,134,202,221,278,310],"Subscript":[57,135,315,321],"Baseline":[59,137,319],"Superscript":[61,330],"i\">":[62],"<mml:mrow>":[64,143,237,284,333],"<mml:mi>a</mml:mi>":[65,98,176,238,290,337],"<mml:mo":[66,69,171,181,239,242,288,291,335,338,341,353],"stretchy=\"false\">(</mml:mo>":[67,240,289,336,342],"<mml:mi>z</mml:mi>":[68,102,241],"stretchy=\"false\">)</mml:mo>":[70,243,292,339,354],"<mml:mo>=</mml:mo>":[71,79,151,286,340],"<mml:munderover>":[72,144],"<mml:mo>":[73,80,145,152,244],"\u2211":[74,146],"</mml:mo>":[75,82,147,154,246],"<mml:mi>i</mml:mi>":[78,99,103,150,174,177,347],"\u2212":[81,153],"mathvariant=\"normal\">":[84,92,156,164,186],"\u221e":[85,93,157,165,187],"</mml:mi>":[86,94,158,166,188],"<mml:mo>+</mml:mo>":[90,162,293],"</mml:munderover>":[96,168],"<mml:msup>":[101],"</mml:msup>":[104],"encoding=\"application/x-tex\">a(z)=\\sum":[107],"_{i=-\\infty":[108,192],"}^{+\\infty":[109,193],"}a_iz^i</mml:annotation>":[110],"such":[114],"that":[115],"alttext=\"sigma-summation":[120],"StartAbsoluteValue":[132],"EndAbsoluteValue":[138],"greater-than":[139],"infinity\">":[141],"stretchy=\"false\">|</mml:mo>":[172,182],"<mml:mo>&gt;</mml:mo>":[184],"encoding=\"application/x-tex\">\\sum":[191],"}|ia_i|&gt;\\infty</mml:annotation>":[194],".":[198],"We":[199],"call":[200],"QT-matrix":[201],"quasi-Toeplitz":[203],"matrix":[204],"alttext=\"upper":[209,272,307],"A\">":[210],"<mml:mi>A</mml:mi>":[212,285],"encoding=\"application/x-tex\">A</mml:annotation>":[214],",":[218,264,301],"associated":[219],"with":[220],"symbol":[222],"element-of":[231,325],"script":[232],"\u2208":[245],"encoding=\"application/x-tex\">a(z)\\in":[258],"\\mathcal":[259],"W_1</mml:annotation>":[260],"A":[273],"T":[276,308],"E\">":[282],"<mml:mi>T</mml:mi>":[287,334],"<mml:mi>E</mml:mi>":[294],"encoding=\"application/x-tex\">A=T(a)+E</mml:annotation>":[297],"where":[302],"t":[314],"comma":[317,323],"j":[318,324],"double-struck":[326],"Z":[328],"Sub":[329],"plus\">":[331],"<mml:mi>t</mml:mi>":[344],"<mml:mo>,</mml:mo>":[348],"<mml:mi>j</mml:mi>":[349]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
