{"id":"https://openalex.org/W2126967844","doi":"https://doi.org/10.1137/140965016","title":"Convergence Rate of Overlapping Domain Decomposition Methods for the Rudin--Osher--Fatemi Model Based on a Dual Formulation","display_name":"Convergence Rate of Overlapping Domain Decomposition Methods for the Rudin--Osher--Fatemi Model Based on a Dual Formulation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2126967844","doi":"https://doi.org/10.1137/140965016","mag":"2126967844"},"language":"en","primary_location":{"id":"doi:10.1137/140965016","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965016","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},"type":"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/A5005718505","display_name":"Huibin Chang","orcid":"https://orcid.org/0000-0002-8833-8940"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huibin Chang","raw_affiliation_strings":["School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, People's Republic of China","institution_ids":["https://openalex.org/I15062923"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":["University of Bergen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":["Nanyang Technological University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101020016","display_name":"Danping Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Danping Yang","raw_affiliation_strings":["[East China Normal University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[East China Normal University]","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8381,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.89233707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"8","issue":"1","first_page":"564","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9950000047683716,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7333250641822815},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6917416453361511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6491445302963257},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6283751130104065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.527456521987915},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5218112468719482},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5017809867858887},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48812589049339294},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4702041745185852},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.46622776985168457},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4629858732223511},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4522450864315033},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39198583364486694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2584245204925537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14345762133598328},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12355849146842957},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.07351893186569214}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7333250641822815},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6917416453361511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6491445302963257},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6283751130104065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.527456521987915},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5218112468719482},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5017809867858887},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48812589049339294},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4702041745185852},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.46622776985168457},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4629858732223511},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4522450864315033},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39198583364486694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2584245204925537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14345762133598328},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12355849146842957},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.07351893186569214},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140965016","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965016","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/107393","is_oa":false,"landing_page_url":"http://hdl.handle.net/10220/25525","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5400000214576721,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1102861184","display_name":null,"funder_award_id":"11071080","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2034748651","display_name":null,"funder_award_id":"11401170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6182734377","display_name":null,"funder_award_id":"U1304610","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8336011166","display_name":null,"funder_award_id":"11426165","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8862120005","display_name":null,"funder_award_id":"11171113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W74071737","https://openalex.org/W155934647","https://openalex.org/W1542243431","https://openalex.org/W1582734821","https://openalex.org/W1758610246","https://openalex.org/W1974705324","https://openalex.org/W1978333359","https://openalex.org/W1981112674","https://openalex.org/W1984648213","https://openalex.org/W1986850130","https://openalex.org/W1989893875","https://openalex.org/W1995537025","https://openalex.org/W2002882465","https://openalex.org/W2003413173","https://openalex.org/W2005089986","https://openalex.org/W2011181254","https://openalex.org/W2016228846","https://openalex.org/W2017085690","https://openalex.org/W2017848200","https://openalex.org/W2018575953","https://openalex.org/W2020461703","https://openalex.org/W2033736734","https://openalex.org/W2052440373","https://openalex.org/W2052972089","https://openalex.org/W2062246266","https://openalex.org/W2062653475","https://openalex.org/W2067736594","https://openalex.org/W2092663520","https://openalex.org/W2095733320","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2104126767","https://openalex.org/W2107604145","https://openalex.org/W2109377842","https://openalex.org/W2114424556","https://openalex.org/W2119159934","https://openalex.org/W2122890444","https://openalex.org/W2129922730","https://openalex.org/W2140581820","https://openalex.org/W2142058898","https://openalex.org/W2151718183","https://openalex.org/W2152612750","https://openalex.org/W2154302251","https://openalex.org/W2156648982","https://openalex.org/W2167400582","https://openalex.org/W2296319761","https://openalex.org/W2314012200","https://openalex.org/W3092559593"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2364594919","https://openalex.org/W1861706286","https://openalex.org/W2219338811","https://openalex.org/W2167092671","https://openalex.org/W2106235829","https://openalex.org/W3169856766","https://openalex.org/W2897217973","https://openalex.org/W2967016861","https://openalex.org/W2132719248"],"abstract_inverted_index":{"This":[0],"paper":[1,90],"is":[2,91,112],"concerned":[3],"with":[4,36],"overlapping":[5,78,130],"domain":[6,152],"decomposition":[7,51,153],"methods":[8],"(DDMs),":[9],"based":[10,80],"on":[11,81,127],"successive":[12],"subspace":[13,18],"correction":[14,19],"(SSC)":[15],"and":[16,100,103,132],"parallel":[17],"(PSC),":[20],"for":[21,151,156],"the":[22,41,50,53,57,82,95,98,105,113,120,124,128,137,157],"Rudin--Osher--Fatemi":[23],"(ROF)":[24],"model":[25],"in":[26,49],"image":[27],"restoration.":[28],"In":[29],"contrast":[30],"to":[31,77,92],"recent":[32],"attempts,":[33],"we":[34,118],"work":[35],"a":[37,62,67,143],"dual":[38,58,83],"formulation":[39],"of":[40,52,56,69,71,88,97,107,115,123,139],"ROF":[42,158],"model,":[43],"where":[44,110],"one":[45],"significant":[46],"difficulty":[47],"resides":[48],"global":[54],"constraint":[55],"variable.":[59],"We":[60],"introduce":[61],"stable":[63],"\u201cunity":[64],"decomposition\u201d":[65],"using":[66],"set":[68],"\u201cpartition":[70],"unity":[72],"functions,\u201d":[73],"which":[74],"naturally":[75],"leads":[76],"DDMs":[79],"formulation.":[84],"The":[85],"main":[86],"objective":[87],"this":[89],"rigorously":[93],"analyze":[94],"convergence":[96,108,125,144],"SSC":[99],"PSC":[101],"algorithms":[102,155],"derive":[104],"rate":[106,126,145],"$O(n^{-1/2})$,":[109],"$n$":[111],"number":[114],"iterations.":[116],"Moreover,":[117],"characterize":[119],"explicit":[121],"dependence":[122],"subdomain":[129],"size":[131],"other":[133],"important":[134],"parameters.":[135],"To":[136],"best":[138],"our":[140],"knowledge,":[141],"such":[142],"has":[146],"not":[147],"yet":[148],"been":[149],"claimed":[150],"related":[154],"model.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
