{"id":"https://openalex.org/W4410605928","doi":"https://doi.org/10.1137/24m1655147","title":"Analysis on Aggregation and Block Smoothers in Multigrid Methods for Block Toeplitz Linear Systems","display_name":"Analysis on Aggregation and Block Smoothers in Multigrid Methods for Block Toeplitz Linear Systems","publication_year":2025,"publication_date":"2025-05-22","ids":{"openalex":"https://openalex.org/W4410605928","doi":"https://doi.org/10.1137/24m1655147"},"language":"en","primary_location":{"id":"doi:10.1137/24m1655147","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1655147","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/A5027199236","display_name":"Matthias Bolten","orcid":"https://orcid.org/0000-0002-8682-7652"},"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":"Matthias Bolten","raw_affiliation_strings":["School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8682-7652","affiliations":[{"raw_affiliation_string":"School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"middle","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. University of Insubria, Como, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7958-9126","affiliations":[{"raw_affiliation_string":"Department of Science and High Technology. University of Insubria, 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/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":false,"raw_author_name":"Paola Ferrari","raw_affiliation_strings":["Department of Mathematics, University of Genoa, Genoa, Italy, and School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6615-7404","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Genoa, Genoa, Italy, and School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083413521","display_name":"Isabella Furci","orcid":"https://orcid.org/0000-0001-8864-6786"},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Isabella Furci","raw_affiliation_strings":["Department of Mathematics, University of Genoa, Genoa, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8864-6786","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Genoa, Genoa, Italy","institution_ids":["https://openalex.org/I83816512"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027199236"],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11954111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"2","first_page":"1416","last_page":"1443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9975000023841858,"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":0.9975000023841858,"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":0.9966999888420105,"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/T11416","display_name":"Numerical methods for differential equations","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.8381029367446899},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8029801249504089},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.675977885723114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5449870228767395},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5365446209907532},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5168631672859192},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3453851044178009},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3447492718696594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3092952370643616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19690024852752686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18948885798454285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8381029367446899},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8029801249504089},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.675977885723114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5449870228767395},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5365446209907532},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5168631672859192},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3453851044178009},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3447492718696594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3092952370643616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19690024852752686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18948885798454285},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/24m1655147","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1655147","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:irinsubria.uninsubria.it:11383/2197514","is_oa":false,"landing_page_url":"https://hdl.handle.net/11383/2197514","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2052391148","display_name":null,"funder_award_id":"PNC-E3-2022-23683267 - Progetto DHEAL-COM - CUP:D33C22001980001","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"}],"funders":[{"id":"https://openalex.org/F4320321781","display_name":"Ministero della Salute","ror":"https://ror.org/00789fa95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W592368443","https://openalex.org/W1087162733","https://openalex.org/W1538769216","https://openalex.org/W1967983557","https://openalex.org/W1975153608","https://openalex.org/W1984747903","https://openalex.org/W1994973976","https://openalex.org/W2015700994","https://openalex.org/W2019204386","https://openalex.org/W2025501795","https://openalex.org/W2057439610","https://openalex.org/W2057901401","https://openalex.org/W2064878022","https://openalex.org/W2078687549","https://openalex.org/W2084784234","https://openalex.org/W2086517326","https://openalex.org/W2125682784","https://openalex.org/W2148147555","https://openalex.org/W2171315210","https://openalex.org/W2498157954","https://openalex.org/W2910646959","https://openalex.org/W3021332721","https://openalex.org/W3113016951","https://openalex.org/W3123821778","https://openalex.org/W3185263971","https://openalex.org/W4242832160","https://openalex.org/W4256359184","https://openalex.org/W4285150684","https://openalex.org/W4366498094","https://openalex.org/W4384464605","https://openalex.org/W4391281404"],"related_works":["https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W151496359","https://openalex.org/W1969863203","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W2171218546","https://openalex.org/W2143448435","https://openalex.org/W2543276709","https://openalex.org/W1964844604"],"abstract_inverted_index":{"We":[0,18,145],"present":[1],"novel":[2],"improvements":[3],"in":[4,176],"the":[5,20,30,42,49,53,56,59,63,67,70,79,95,101,112,118,147,155,161],"context":[6],"of":[7,22,32,48,58,69,81,103,114,157],"symbol-based":[8],"multigrid":[9,84],"procedures":[10],"for":[11,90,106,185],"solving":[12],"large":[13],"block":[14,34,107,115,120,186],"structured":[15,187],"linear":[16,151,188],"systems.":[17,189],"study":[19],"application":[21],"an":[23],"aggregation-based":[24],"grid":[25,87],"transfer":[26,88],"operator":[27],"that":[28],"transforms":[29],"symbol":[31,61],"a":[33,82],"Toeplitz":[35,92,108],"matrix":[36],"from":[37,154],"matrix-valued":[38,72],"to":[39,77,182],"scalar-valued":[40,60],"at":[41,62,94],"coarser":[43,64,96],"level.":[44],"Our":[45],"convergence":[46,80],"analysis":[47],"two-grid":[50],"method":[51,166],"reveals":[52],"connection":[54],"between":[55],"features":[57],"level":[65],"and":[66],"properties":[68],"original":[71],"one.":[73],"This":[74],"allows":[75],"us":[76],"prove":[78],"V-cycle":[83],"with":[85,130,141,160,169],"standard":[86],"operators":[89],"scalar":[91],"systems":[93,152],"levels.":[97],"Consequently,":[98],"we":[99],"extend":[100],"class":[102],"suitable":[104],"smoothers":[105],"matrices,":[109],"focusing":[110],"on":[111,125,132,150],"efficiency":[113],"strategies,":[116],"particularly":[117],"relaxed":[119],"Jacobi":[121],"method.":[122],"General":[123],"conditions":[124],"smoothing":[126],"parameters":[127,137],"are":[128],"derived,":[129],"emphasis":[131],"practical":[133],"applications":[134],"where":[135],"these":[136],"can":[138],"be":[139],"calculated":[140],"negligible":[142],"computational":[143,179],"cost.":[144],"test":[146],"proposed":[148],"strategies":[149],"stemming":[153],"discretization":[156],"differential":[158],"problems":[159],"\\BbbQd":[162],"Lagrangian":[163],"finite":[164],"element":[165],"or":[167],"B-spline":[168],"nonmaximal":[170],"regularity.":[171],"The":[172],"numerical":[173],"results":[174],"show":[175],"both":[177],"cases":[178],"advantages":[180],"compared":[181],"existing":[183],"methods":[184]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
