{"id":"https://openalex.org/W2001907494","doi":"https://doi.org/10.1137/050627046","title":"Two-level Toeplitz preconditioning: approximation results for matrices and functions","display_name":"Two-level Toeplitz preconditioning: approximation results for matrices and functions","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2001907494","doi":"https://doi.org/10.1137/050627046","mag":"2001907494"},"language":"en","primary_location":{"id":"doi:10.1137/050627046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627046","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5008198354","display_name":"D. Noutsos","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. Noutsos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"S. Serra Capizzano","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Serra Capizzano","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078840132","display_name":"Paris Vassalos","orcid":"https://orcid.org/0000-0002-2131-7643"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Vassalos","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008198354"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.677,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.69503926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"2","first_page":"439","last_page":"458"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9132781624794006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7882142066955566},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6498931050300598},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5359986424446106},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5108854174613953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5065017938613892},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4815923869609833},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45670080184936523},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.4527752995491028},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4501188397407532},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3707883656024933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2282131016254425},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12345269322395325},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0705292820930481}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9132781624794006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7882142066955566},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6498931050300598},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5359986424446106},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5108854174613953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5065017938613892},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4815923869609833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45670080184936523},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.4527752995491028},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4501188397407532},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3707883656024933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2282131016254425},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12345269322395325},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0705292820930481},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050627046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627046","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/1494925","is_oa":false,"landing_page_url":"http://hdl.handle.net/11383/1494925","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W605044866","https://openalex.org/W1511121222","https://openalex.org/W1550150926","https://openalex.org/W1580112161","https://openalex.org/W1967122689","https://openalex.org/W1969578814","https://openalex.org/W1970334228","https://openalex.org/W1975357829","https://openalex.org/W1988177606","https://openalex.org/W1994176509","https://openalex.org/W1999875980","https://openalex.org/W2003977554","https://openalex.org/W2004165073","https://openalex.org/W2005041367","https://openalex.org/W2006850990","https://openalex.org/W2008324087","https://openalex.org/W2014870838","https://openalex.org/W2015700994","https://openalex.org/W2018836136","https://openalex.org/W2024597248","https://openalex.org/W2040145533","https://openalex.org/W2054781018","https://openalex.org/W2055980435","https://openalex.org/W2064616889","https://openalex.org/W2068285024","https://openalex.org/W2083971164","https://openalex.org/W2086989241","https://openalex.org/W2098704097","https://openalex.org/W2134572726","https://openalex.org/W2136826453","https://openalex.org/W2162176806","https://openalex.org/W2326028551","https://openalex.org/W3032164133","https://openalex.org/W4239165712"],"related_works":["https://openalex.org/W151496359","https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W1969863203","https://openalex.org/W2143448435","https://openalex.org/W4247704229","https://openalex.org/W4225411471","https://openalex.org/W582364689"],"abstract_inverted_index":{"Large":[0],"2-level":[1,92],"Toeplitz":[2],"systems":[3],"arise":[4],"in":[5,60,73,125],"a":[6,96],"variety":[7],"of":[8,42,47,101,104,114],"applications":[9],"(see,":[10],"e.g.,":[11],"[R.":[12],"H.":[13],"Chan":[14],"and":[15,68,79,123],"M.":[16],"Ng,":[17],"SIAM":[18],"Rev.,":[19],"38":[20],"(1996),":[21],"pp.":[22,88],"427-482])":[23],"for":[24,29,90,111],"which":[25],"efficient":[26],"numerical":[27,36,119],"methods":[28],"their":[30],"solution":[31,113],"are":[32,121],"required.":[33],"Some":[34],"successful":[35],"techniques":[37],"need":[38],"the":[39,43,48,70,91,99,102,112],"explicit":[40],"knowledge":[41,100],"generating":[44],"function":[45],"f":[46],"considered":[49],"system":[50],"$T_{n}(f){\\rm":[51],"x}=b$,":[52],"an":[53],"assumption":[54],"that":[55],"usually":[56],"is":[57],"not":[58],"fulfilled":[59],"real":[61],"applications.":[62],"In":[63,94],"this":[64],"paper":[65],"we":[66,106],"analyze":[67],"complete":[69],"procedure":[71],"proposed":[72],"[D.":[74],"Noutsas,":[75],"S.":[76],"Serra":[77],"Capizzano,":[78],"P.":[80],"Vassalos,":[81],"Numer.":[82],"Linear":[83],"Algebra":[84],"Appl.,":[85],"12":[86],"(2005),":[87],"231-239]":[89],"case.":[93],"such":[95],"way,":[97],"from":[98],"coefficients":[103],"$T_{n}(f)$,":[105],"determine":[107],"optimal":[108],"preconditioning":[109],"strategies":[110],"our":[115,128],"systems.":[116],"Finally,":[117],"some":[118],"experiments":[120],"performed":[122],"discussed":[124],"connection":[126],"with":[127],"theoretical":[129],"analysis.":[130]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}
