{"id":"https://openalex.org/W3113016951","doi":"https://doi.org/10.1002/nla.2356","title":"Multigrid methods for block\u2010Toeplitz linear systems: convergence analysis and applications","display_name":"Multigrid methods for block\u2010Toeplitz linear systems: convergence analysis and applications","publication_year":2020,"publication_date":"2020-12-17","ids":{"openalex":"https://openalex.org/W3113016951","doi":"https://doi.org/10.1002/nla.2356","mag":"3113016951"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2356","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2356","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009786921","display_name":"Marco Donatelli","orcid":"https://orcid.org/0000-0001-7958-9126"},"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":"Marco Donatelli","raw_affiliation_strings":["Department of Science and High Technology, Insubria University, Como, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Science and High Technology, Insubria University, Como, Italy","institution_ids":["https://openalex.org/I115752224"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101782477","display_name":"Paola Ferrari","orcid":"https://orcid.org/0000-0001-6615-7404"},"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":"Paola Ferrari","raw_affiliation_strings":["Department of Science and High Technology, Insubria University, Como, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Science and High Technology, Insubria University, Como, Italy","institution_ids":["https://openalex.org/I115752224"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083413521","display_name":"Isabella Furci","orcid":"https://orcid.org/0000-0001-8864-6786"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Isabella Furci","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Wuppertal, Wuppertal, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053268193","display_name":"Stefano Serra\u2010Capizzano","orcid":"https://orcid.org/0000-0001-9477-109X"},"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":"Stefano Serra\u2010Capizzano","raw_affiliation_strings":["Department of Humanities and Innovation, Insubria University, Como, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Humanities and Innovation, Insubria University, Como, Italy","institution_ids":["https://openalex.org/I115752224"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052976118","display_name":"Debora Sesana","orcid":null},"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":"Debora Sesana","raw_affiliation_strings":["Department of Science and High Technology, Insubria University, Como, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Science and High Technology, Insubria University, Como, Italy","institution_ids":["https://openalex.org/I115752224"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083413521"],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"apc_paid":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"fwci":0.91,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":10,"citation_normalized_percentile":{"value":0.606079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":86,"max":87},"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9996,"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":0.9996,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9957,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transfer-operator","display_name":"Transfer operator","score":0.6972106},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6412197}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8286743},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.6972106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66662645},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6412197},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5502116},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.54133403},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5067137},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5053471},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4355918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3390687},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32563132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2508133},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.17779374},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.122356355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11706242},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07460374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07356587},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2356","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2356","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1910.13792","pdf_url":"https://arxiv.org/pdf/1910.13792","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2356","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2356","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":22,"referenced_works":["https://openalex.org/W1087162733","https://openalex.org/W1970334228","https://openalex.org/W1975153608","https://openalex.org/W1984045033","https://openalex.org/W1994973976","https://openalex.org/W2015700994","https://openalex.org/W2020954443","https://openalex.org/W2056645965","https://openalex.org/W2057439610","https://openalex.org/W2066660517","https://openalex.org/W2068535332","https://openalex.org/W2085547810","https://openalex.org/W2086517326","https://openalex.org/W2155713156","https://openalex.org/W2170392325","https://openalex.org/W2171315210","https://openalex.org/W2283904712","https://openalex.org/W2498157954","https://openalex.org/W2613904156","https://openalex.org/W2621397604","https://openalex.org/W2789730805","https://openalex.org/W4230843528"],"related_works":["https://openalex.org/W78997912","https://openalex.org/W3033387009","https://openalex.org/W2543276709","https://openalex.org/W2493281735","https://openalex.org/W2377164732","https://openalex.org/W2171218546","https://openalex.org/W2143448435","https://openalex.org/W2023923962","https://openalex.org/W2014327818","https://openalex.org/W1991081991"],"abstract_inverted_index":{"Abstract":[0],"In":[1,49,73,104],"the":[2,23,31,37,52,55,90,94,106,109,118,133,137,143,154,175,181,197,201,207,210],"past":[3],"decades,":[4],"multigrid":[5,166],"methods":[6,188,193],"for":[7,169],"linear":[8],"systems":[9],"having":[10],"multilevel":[11],"Toeplitz":[12],"coefficient":[13],"matrices":[14,42,100],"with":[15,69,101],"scalar":[16,119],"entries":[17,38],"have":[18,29,57,125],"been":[19,58],"widely":[20],"studied.":[21],"On":[22],"other":[24],"hand,":[25],"only":[26],"few":[27],"papers":[28],"investigated":[30],"case":[32,51,95,120],"of":[33,43,47,54,89,96,108,117,136,149,203,209],"block":[34,134],"entries,":[35],"where":[36],"are":[39,194],"small":[40],"generic":[41,102],"fixed":[44],"size":[45],"instead":[46],"scalars.":[48],"that":[50,178],"efforts":[53],"researchers":[56],"mainly":[59],"devoted":[60],"to":[61,126,142,163,180],"specific":[62,129],"applications,":[63],"focusing":[64],"on":[65,132],"algorithmic":[66],"proposals,":[67],"but":[68],"marginal":[70],"theoretical":[71,156,212],"results.":[72],"this":[74],"paper,":[75],"we":[76,124,145,159],"propose":[77,160],"a":[78,114,128,147,161],"general":[79],"two\u2010grid":[80],"convergence":[81,86,167],"analysis,":[82,144],"proving":[83],"an":[84],"optimal":[85],"rate":[87],"independent":[88],"matrix":[91],"size,":[92],"in":[93,122,196],"positive":[97],"definite":[98],"block\u2010Toeplitz":[99,182],"blocks.":[103],"particular,":[105],"proof":[107],"approximation":[110],"property":[111],"is":[112],"not":[113],"straightforward":[115],"generalization":[116],"and,":[121],"fact,":[123],"require":[127],"commutativity":[130],"condition":[131],"symbol":[135],"grid":[138,150],"transfer":[139,151],"operator.":[140],"According":[141],"define":[146],"class":[148],"operators":[152],"satisfying":[153],"previous":[155],"conditions":[157],"and":[158,189,206],"strategy":[162],"ensure":[164],"fast":[165],"even":[168],"more":[170],"than":[171],"two":[172],"grids.":[173],"Among":[174],"numerous":[176],"applications":[177],"lead":[179],"structure,":[183],"high\u2010order":[184],"Lagrangian":[185],"finite":[186],"element":[187],"staggered":[190],"discontinuous":[191],"Galerkin":[192],"considered":[195],"numerical":[198],"results,":[199],"confirming":[200],"effectiveness":[202],"our":[204],"proposal":[205],"correctness":[208],"proposed":[211],"analysis.":[213]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3113016951","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3}],"updated_date":"2025-01-21T05:20:40.881506","created_date":"2020-12-21"}