{"id":"https://openalex.org/W4283026013","doi":"https://doi.org/10.1007/s00211-022-01300-4","title":"Convergence rates of a dual gradient method for constrained linear ill-posed problems","display_name":"Convergence rates of a dual gradient method for constrained linear ill-posed problems","publication_year":2022,"publication_date":"2022-06-22","ids":{"openalex":"https://openalex.org/W4283026013","doi":"https://doi.org/10.1007/s00211-022-01300-4"},"language":"lv","primary_location":{"id":"doi:10.1007/s00211-022-01300-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01300-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01300-4.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01300-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101410597","display_name":"Qinian Jin","orcid":"https://orcid.org/0000-0001-9283-9791"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Qinian Jin","raw_affiliation_strings":["Mathematical Sciences Institute, Australian National University, Canberra, ACT, 2601, Australia"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, Australian National University, Canberra, ACT, 2601, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101410597"],"corresponding_institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":5.4417,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.97402342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"151","issue":"4","first_page":"841","last_page":"871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/algorithm","display_name":"Algorithm","score":0.637569785118103},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47448304295539856},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.47038331627845764},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4679763615131378},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41813924908638},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39419665932655334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.381369411945343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1966780126094818}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.637569785118103},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47448304295539856},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47038331627845764},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4679763615131378},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41813924908638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39419665932655334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.381369411945343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1966780126094818},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-022-01300-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01300-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01300-4.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/307343","is_oa":true,"landing_page_url":"http://hdl.handle.net/1885/307343","pdf_url":"https://openresearch-repository.anu.edu.au/bitstreams/d0d92d08-d219-4315-ba29-882d354e62a2/download","source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1007/s00211-022-01300-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01300-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01300-4.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320431","display_name":"Australian National University","ror":"https://ror.org/019wvm592"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283026013.pdf","grobid_xml":"https://content.openalex.org/works/W4283026013.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W632810616","https://openalex.org/W1570089119","https://openalex.org/W1837565340","https://openalex.org/W1913729665","https://openalex.org/W1965676116","https://openalex.org/W1970986119","https://openalex.org/W1989436614","https://openalex.org/W1993118533","https://openalex.org/W1993227605","https://openalex.org/W2004632554","https://openalex.org/W2009877468","https://openalex.org/W2035197597","https://openalex.org/W2036838083","https://openalex.org/W2037994867","https://openalex.org/W2038948856","https://openalex.org/W2039466093","https://openalex.org/W2060041011","https://openalex.org/W2062460234","https://openalex.org/W2070030655","https://openalex.org/W2080888649","https://openalex.org/W2095582900","https://openalex.org/W2100556411","https://openalex.org/W2114605231","https://openalex.org/W2136334809","https://openalex.org/W2139665062","https://openalex.org/W2165256533","https://openalex.org/W2176777789","https://openalex.org/W2301820320","https://openalex.org/W2304430533","https://openalex.org/W2558436941","https://openalex.org/W2562805810","https://openalex.org/W2673237422","https://openalex.org/W2763081248","https://openalex.org/W2771952784","https://openalex.org/W2789242774","https://openalex.org/W2949294682","https://openalex.org/W2963398839","https://openalex.org/W2965795320","https://openalex.org/W3019623890","https://openalex.org/W3098222293","https://openalex.org/W3098416719","https://openalex.org/W3098979341","https://openalex.org/W3099782645","https://openalex.org/W3100376956","https://openalex.org/W3100706439","https://openalex.org/W3102819058","https://openalex.org/W3105695370","https://openalex.org/W3121459423","https://openalex.org/W3150750315","https://openalex.org/W3156003168","https://openalex.org/W4213046749","https://openalex.org/W4298264214"],"related_works":["https://openalex.org/W2278466645","https://openalex.org/W2136053165","https://openalex.org/W2042726902","https://openalex.org/W2018828049","https://openalex.org/W1598979804","https://openalex.org/W3102909640","https://openalex.org/W2323683917","https://openalex.org/W2046712581","https://openalex.org/W2370340664","https://openalex.org/W2049276036"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"consider":[5,107],"a":[6,45,50,55,72,97],"dual":[7],"gradient":[8],"method":[9,69,91,112],"for":[10],"solving":[11],"linear":[12,47],"ill-posed":[13],"problems":[14],"$$Ax":[15],"=":[16],"y$$":[17],"<mml:math":[18,34],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19,35],"<mml:mrow>":[20,36],"<mml:mi>A</mml:mi>":[21,37],"<mml:mi>x</mml:mi>":[22],"<mml:mo>=</mml:mo>":[23],"<mml:mi>y</mml:mi>":[24],"</mml:mrow>":[25,42],"</mml:math>":[26,43],",":[27],"where":[28],"$$A":[29],":":[30],"X":[31,53],"\\rightarrow":[32],"Y$$":[33],"<mml:mo>:</mml:mo>":[38],"<mml:mi>X</mml:mi>":[39],"<mml:mo>\u2192</mml:mo>":[40],"<mml:mi>Y</mml:mi>":[41],"is":[44,65,92],"bounded":[46],"operator":[48],"from":[49],"Banach":[51],"space":[52,57],"to":[54,70],"Hilbert":[56],"Y":[58],".":[59],"A":[60],"strongly":[61],"convex":[62],"penalty":[63],"function":[64],"used":[66],"in":[67],"the":[68,82,90,102,111],"select":[71],"solution":[73],"with":[74],"desired":[75],"feature.":[76],"Under":[77],"variational":[78],"source":[79],"conditions":[80],"on":[81],"sought":[83],"solution,":[84],"convergence":[85],"rates":[86],"are":[87],"derived":[88],"when":[89],"terminated":[93],"by":[94],"either":[95],"an":[96,108],"priori":[98],"stopping":[99],"rule":[100],"or":[101],"discrepancy":[103],"principle.":[104],"We":[105],"also":[106],"acceleration":[109],"of":[110],"as":[113,115],"well":[114],"its":[116],"various":[117],"applications.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
