{"id":"https://openalex.org/W2092466425","doi":"https://doi.org/10.1137/s0036142903430906","title":"Analysis of Regularization Methods for the Solution of Ill-Posed Problems Involving Discontinuous Operators","display_name":"Analysis of Regularization Methods for the Solution of Ill-Posed Problems Involving Discontinuous Operators","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2092466425","doi":"https://doi.org/10.1137/s0036142903430906","mag":"2092466425"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903430906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903430906","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.06999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"F. Fr\u00fchauf","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Fr\u00fchauf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"O. Scherzer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"O. Scherzer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"A. Leit\u00e3o","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Leit\u00e3o","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0693,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.94578384,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"2","first_page":"767","last_page":"786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9771999716758728,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9771999716758728,"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"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.008700000122189522,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/regularization","display_name":"Regularization (linguistics)","score":0.7565000057220459},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5562999844551086},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.5156999826431274},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46889999508857727},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4311000108718872},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.33160001039505005}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7565000057220459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7458999752998352},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5562999844551086},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5149000287055969},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46889999508857727},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33889999985694885},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32820001244544983},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.29670000076293945},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27649998664855957},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142903430906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903430906","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.06999","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.06999","pdf_url":"https://arxiv.org/pdf/2011.06999","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.06999","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.06999","pdf_url":"https://arxiv.org/pdf/2011.06999","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W604456982","https://openalex.org/W1578255497","https://openalex.org/W1991113069","https://openalex.org/W2017848200","https://openalex.org/W2022653706","https://openalex.org/W2022816471","https://openalex.org/W2029997366","https://openalex.org/W2032472399","https://openalex.org/W2041494914","https://openalex.org/W2042226984","https://openalex.org/W2045433475","https://openalex.org/W2080050826","https://openalex.org/W2081774672","https://openalex.org/W2095365402","https://openalex.org/W2098109295","https://openalex.org/W2120876740","https://openalex.org/W2132363464","https://openalex.org/W2139374946","https://openalex.org/W2159451621","https://openalex.org/W4230752651","https://openalex.org/W4250073828"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,18,21,34],"regularization":[3,42,67],"concept":[4],"for":[5],"the":[6,13,54,64,78,81],"solution":[7],"of":[8,17,36,45,56,63,80],"ill-posed":[9],"operator":[10,14],"equations,":[11],"where":[12,31],"is":[15,27,43,58,69,74,84],"composed":[16],"continuous":[19],"and":[20,77],"discontinuous":[22],"operator.":[23],"A":[24,49],"particular":[25],"application":[26],"level":[28,40,65],"set":[29,41,66],"regularization,":[30],"we":[32],"develop":[33],"novelconcept":[35],"minimizers.":[37],"The":[38,60],"proposed":[39,82],"capable":[44],"handling":[46],"changing":[47],"topologies.":[48],"functional":[50],"analytic":[51],"framework":[52],"explaining":[53],"splitting":[55],"topologies":[57],"given.":[59],"asymptotic":[61],"limit":[62],"method":[68],"an":[70,88],"evolution":[71],"process,":[72],"which":[73],"implemented":[75],"numerically,":[76],"quality":[79],"algorithm":[83],"demonstrated":[85],"by":[86],"solving":[87],"inverse":[89],"source":[90],"problem.":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}