{"id":"https://openalex.org/W2945728267","doi":"https://doi.org/10.1137/19m1263066","title":"Convergence of Heuristic Parameter Choice Rules for Convex Tikhonov Regularization","display_name":"Convergence of Heuristic Parameter Choice Rules for Convex Tikhonov Regularization","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2945728267","doi":"https://doi.org/10.1137/19m1263066","mag":"2945728267"},"language":"en","primary_location":{"id":"doi:10.1137/19m1263066","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263066","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/1905.06828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Stefan Kindermann","orcid":"https://orcid.org/0000-0002-3688-5125"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stefan Kindermann","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Kemal Raik","orcid":"https://orcid.org/0000-0002-3972-5565"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kemal Raik","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.738,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89500734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"58","issue":"3","first_page":"1773","last_page":"1800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.8981999754905701,"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":0.8981999754905701,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.06289999932050705,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.8424000144004822},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6304000020027161},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5963000059127808},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5910000205039978},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5309000015258789},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5085999965667725},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4934000074863434},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.44850000739097595}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.8424000144004822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7710999846458435},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6304000020027161},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5963000059127808},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5309000015258789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5199000239372253},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49939998984336853},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.44850000739097595},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4269999861717224},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4171000123023987},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3977000117301941},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3467999994754791},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2840999960899353},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.2603999972343445}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1263066","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263066","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:1905.06828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.06828","pdf_url":"https://arxiv.org/pdf/1905.06828","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:1905.06828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.06828","pdf_url":"https://arxiv.org/pdf/1905.06828","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":[{"id":"https://openalex.org/G8593049717","display_name":null,"funder_award_id":"P 30157-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1993118533","https://openalex.org/W1993692881","https://openalex.org/W1995713983","https://openalex.org/W1998762105","https://openalex.org/W2002384352","https://openalex.org/W2011181254","https://openalex.org/W2012016993","https://openalex.org/W2023206259","https://openalex.org/W2033468335","https://openalex.org/W2072378378","https://openalex.org/W2088955745","https://openalex.org/W2090376964","https://openalex.org/W2100556411","https://openalex.org/W2120156893","https://openalex.org/W2145962863","https://openalex.org/W2314826591","https://openalex.org/W2318147017","https://openalex.org/W2415338358","https://openalex.org/W2562805810","https://openalex.org/W2758399669","https://openalex.org/W2885970858","https://openalex.org/W2890208036","https://openalex.org/W2950042078","https://openalex.org/W2963812766"],"related_works":[],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,32,37,56,66,73,83],"convergence":[3,57,71,78],"theory":[4,79],"of":[5,22,59,72,85],"several":[6],"known":[7],"as":[8,10],"well":[9,43],"new":[11],"heuristic":[12,60],"parameter":[13],"choice":[14],"rules":[15,61],"for":[16,47,82],"convex":[17,67],"Tikhonov":[18],"regularization.":[19],"The":[20,77],"success":[21],"such":[23,40],"methods":[24,75],"is":[25,80],"dependent":[26],"on":[27,31],"whether":[28],"certain":[29],"restrictions":[30,64],"noise":[33,63],"are":[34,42],"satisfied.":[35],"In":[36,51],"linear":[38],"theory,":[39],"conditions":[41],"understood":[44],"and":[45,69],"hold":[46],"typically":[48],"irregular":[49],"noise.":[50],"this":[52],"paper,":[53],"we":[54],"extend":[55],"analysis":[58],"using":[62],"to":[65],"setting":[68],"prove":[70],"aforementioned":[74],"therewith.":[76],"exemplified":[81],"case":[84],"an":[86],"ill-posed":[87],"problem":[88],"with":[89],"a":[90],"diagonal":[91],"forward":[92],"operator":[93],"in":[94],"$\\ell^q$":[95],"spaces.":[96],"Numerical":[97],"examples":[98],"also":[99],"provide":[100],"further":[101],"insight.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2019-05-29T00:00:00"}
