{"id":"https://openalex.org/W3089665431","doi":"https://doi.org/10.1002/nla.2335","title":"On the numerical solution of ill\u2010conditioned linear systems by regularization and iteration","display_name":"On the numerical solution of ill\u2010conditioned linear systems by regularization and iteration","publication_year":2020,"publication_date":"2020-09-28","ids":{"openalex":"https://openalex.org/W3089665431","doi":"https://doi.org/10.1002/nla.2335","mag":"3089665431"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2335","pdf_url":null,"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_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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5055014506","display_name":"Renato Spigler","orcid":"https://orcid.org/0000-0002-4561-4845"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Renato Spigler","raw_affiliation_strings":["Department of Mathematics and Physics, Roma Tre University, Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Roma Tre University, Roma, Italy","institution_ids":["https://openalex.org/I119003972"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055014506"],"corresponding_institution_ids":["https://openalex.org/I119003972"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"apc_paid":null,"fwci":0.114,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.549694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":69,"max":73},"biblio":{"volume":"28","issue":"1","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":0.9999,"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":0.9999,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9987,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9984,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization","score":0.64134336},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.5914138},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5387453},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45975232}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.8526353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.81756854},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6606621},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.64134336},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.5914138},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.59118146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.57900524},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5663767},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5387453},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5306227},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45975232},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.45945412},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43603542},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4180316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36786443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31256795},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.22484198},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.13830227},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12586296},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.063604385},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2335","pdf_url":null,"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_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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":21,"referenced_works":["https://openalex.org/W1940321820","https://openalex.org/W1981220107","https://openalex.org/W2009511046","https://openalex.org/W2018792828","https://openalex.org/W2019787708","https://openalex.org/W2021311647","https://openalex.org/W2067291657","https://openalex.org/W2077179019","https://openalex.org/W2080201523","https://openalex.org/W2114301203","https://openalex.org/W2128132991","https://openalex.org/W2141870784","https://openalex.org/W2325176464","https://openalex.org/W2335013895","https://openalex.org/W2569133694","https://openalex.org/W2609118327","https://openalex.org/W2739243443","https://openalex.org/W2792845377","https://openalex.org/W4237219696","https://openalex.org/W4292025407","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W66239430","https://openalex.org/W3017856821","https://openalex.org/W2950382084","https://openalex.org/W2373060551","https://openalex.org/W2366095940","https://openalex.org/W2349582882","https://openalex.org/W2238761578","https://openalex.org/W2169021366","https://openalex.org/W2081925639","https://openalex.org/W2044939737"],"abstract_inverted_index":{"Summary":[0],"We":[1],"propose":[2],"to":[3,20,35],"reduce":[4],"the":[5,21,37,40,78],"(spectral)":[6],"condition":[7],"number":[8],"of":[9,39,45,85],"a":[10,16,82],"given":[11],"linear":[12],"system":[13,22],"by":[14,26],"adding":[15],"suitable":[17],"diagonal":[18],"matrix":[19],"matrix,":[23],"in":[24,53],"particular":[25],"shifting":[27],"its":[28],"spectrum.":[29],"Iterative":[30],"procedures":[31],"are":[32,59],"then":[33],"adopted":[34],"recover":[36],"solution":[38],"original":[41],"system.":[42],"The":[43],"case":[44],"real":[46],"symmetric":[47],"positive":[48],"definite":[49],"matrices":[50],"is":[51],"considered":[52],"particular,":[54],"and":[55,70],"several":[56],"numerical":[57],"examples":[58],"given.":[60],"This":[61],"approach":[62],"has":[63],"some":[64],"close":[65],"relations":[66],"with":[67,71,81],"Riley's":[68],"method":[69],"Tikhonov":[72],"regularization.":[73],"Moreover,":[74],"we":[75],"identify":[76],"approximately":[77],"aforementioned":[79],"procedure":[80],"true":[83],"action":[84],"preconditioning.":[86]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3089665431","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2024-12-28T23:24:50.709587","created_date":"2020-10-08"}