{"id":"https://openalex.org/W1976727549","doi":"https://doi.org/10.1090/s0025-5718-2012-02596-8","title":"A convergence analysis of regularization by discretization in preimage space","display_name":"A convergence analysis of regularization by discretization in preimage space","publication_year":2012,"publication_date":"2012-04-02","ids":{"openalex":"https://openalex.org/W1976727549","doi":"https://doi.org/10.1090/s0025-5718-2012-02596-8","mag":"1976727549"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02596-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02596-8","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02596-8/S0025-5718-2012-02596-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02596-8/S0025-5718-2012-02596-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011058927","display_name":"Barbara Kaltenbacher","orcid":"https://orcid.org/0000-0002-3295-6977"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]},{"id":"https://openalex.org/I134023368","display_name":"Institute for Interdisciplinary Studies of Austrian Universities","ror":"https://ror.org/001zf8v27","country_code":"AT","type":"education","lineage":["https://openalex.org/I134023368","https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Barbara Kaltenbacher","raw_affiliation_strings":["Institute for Mathematics, University of Klagenfurt, Universit\u00c3\u00a4tsstra\u00c3\u009fe 65-67, A-9020 Klagenfurt, Austria","Institute for Mathematics, University of Klagenfurt, Universit\u00e4tsstra\u00dfe 65-67, A-9020 Klagenfurt, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, University of Klagenfurt, Universit\u00c3\u00a4tsstra\u00c3\u009fe 65-67, A-9020 Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]},{"raw_affiliation_string":"Institute for Mathematics, University of Klagenfurt, Universit\u00e4tsstra\u00dfe 65-67, A-9020 Klagenfurt, Austria","institution_ids":["https://openalex.org/I134023368"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065088520","display_name":"Jonas Offtermatt","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jonas Offtermatt","raw_affiliation_strings":["Institute for Stochastics and Applications, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Stochastics and Applications, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011058927"],"corresponding_institution_ids":["https://openalex.org/I134023368","https://openalex.org/I4210166741"],"apc_list":null,"apc_paid":null,"fwci":2.0951,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.83933184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"81","issue":"280","first_page":"2049","last_page":"2069"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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":1.0,"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":0.9860000014305115,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/discretization","display_name":"Discretization","score":0.9132510423660278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8705736398696899},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7762008905410767},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6634743213653564},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6169369220733643},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.5538238883018494},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46475234627723694},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.44271016120910645},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3451932370662689},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3451669216156006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10957774519920349}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.9132510423660278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8705736398696899},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7762008905410767},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6634743213653564},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6169369220733643},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.5538238883018494},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46475234627723694},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.44271016120910645},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3451932370662689},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3451669216156006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10957774519920349},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02596-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02596-8","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02596-8/S0025-5718-2012-02596-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02596-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02596-8","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02596-8/S0025-5718-2012-02596-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G523492319","display_name":null,"funder_award_id":"EXC 310","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6039471144","display_name":null,"funder_award_id":"EXC 310/1","funder_id":"https://openalex.org/F4320325850","funder_display_name":"Universit\u00e4t Stuttgart"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6468402549","display_name":null,"funder_award_id":"EXC 310/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325850","display_name":"Universit\u00e4t Stuttgart","ror":"https://ror.org/04vnq7t77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1976727549.pdf","grobid_xml":"https://content.openalex.org/works/W1976727549.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W187546249","https://openalex.org/W297194445","https://openalex.org/W335285985","https://openalex.org/W1487778842","https://openalex.org/W1531455566","https://openalex.org/W1539945301","https://openalex.org/W1545334034","https://openalex.org/W1564864701","https://openalex.org/W1570089119","https://openalex.org/W1586623601","https://openalex.org/W1974815257","https://openalex.org/W1975612171","https://openalex.org/W1982042384","https://openalex.org/W1985999777","https://openalex.org/W1992575806","https://openalex.org/W1996326731","https://openalex.org/W2022816471","https://openalex.org/W2026102280","https://openalex.org/W2036369379","https://openalex.org/W2039674382","https://openalex.org/W2058204667","https://openalex.org/W2058583833","https://openalex.org/W2060819023","https://openalex.org/W2065759858","https://openalex.org/W2076303921","https://openalex.org/W2080888649","https://openalex.org/W2083244588","https://openalex.org/W2120399646","https://openalex.org/W2133560833","https://openalex.org/W2330399463","https://openalex.org/W2795407492","https://openalex.org/W4247385000","https://openalex.org/W4292361795","https://openalex.org/W4292414053","https://openalex.org/W4299416517","https://openalex.org/W4302620827"],"related_works":["https://openalex.org/W37066597","https://openalex.org/W25733641","https://openalex.org/W1977553163","https://openalex.org/W1993570899","https://openalex.org/W188298612","https://openalex.org/W1555094802","https://openalex.org/W3128822846","https://openalex.org/W4230197975","https://openalex.org/W2028070877","https://openalex.org/W2046814020"],"abstract_inverted_index":{"In":[0],"this":[1,37],"paper":[2],"we":[3,52],"investigate":[4],"the":[5,27,60],"regularizing":[6],"properties":[7],"of":[8],"discretization":[9,28],"in":[10,36],"preimage":[11],"space":[12],"for":[13],"linear":[14],"and":[15],"nonlinear":[16],"ill-posed":[17],"operator":[18],"equations":[19],"with":[20],"noisy":[21],"data.":[22],"We":[23],"propose":[24],"to":[25,50],"choose":[26],"level,":[29],"that":[30],"acts":[31],"as":[32],"a":[33,40],"regularization":[34],"parameter":[35],"context,":[38],"by":[39],"discrepancy":[41],"principle.":[42],"While":[43],"general":[44],"convergence":[45,54],"has":[46],"been":[47],"shown":[48],"not":[49],"hold,":[51],"provide":[53],"results":[55],"under":[56],"appropriate":[57],"conditions":[58],"on":[59],"exact":[61],"solution.":[62]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}