{"id":"https://openalex.org/W2071486596","doi":"https://doi.org/10.1137/130919398","title":"Convergence Analysis for Anderson Acceleration","display_name":"Convergence Analysis for Anderson Acceleration","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2071486596","doi":"https://doi.org/10.1137/130919398","mag":"2071486596"},"language":"en","primary_location":{"id":"doi:10.1137/130919398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130919398","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":["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/A5002140195","display_name":"Alex Toth","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alex Toth","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036627173","display_name":"C. T. Kelley","orcid":"https://orcid.org/0000-0003-2791-0648"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. T. Kelley","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002140195"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":17.2069,"has_fulltext":false,"cited_by_count":205,"citation_normalized_percentile":{"value":0.99526907,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"53","issue":"2","first_page":"805","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.998199999332428,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9818999767303467,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8319936394691467},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.7557965517044067},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6650930643081665},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.5676548480987549},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.5564655065536499},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5553542375564575},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5433372855186462},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.49583491683006287},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39764896035194397},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0554870069026947}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8319936394691467},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.7557965517044067},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6650930643081665},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.5676548480987549},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.5564655065536499},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5553542375564575},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5433372855186462},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.49583491683006287},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39764896035194397},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0554870069026947},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"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":1,"locations":[{"id":"doi:10.1137/130919398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130919398","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W21461112","https://openalex.org/W1490604220","https://openalex.org/W1523709528","https://openalex.org/W1708984004","https://openalex.org/W1965440550","https://openalex.org/W1966801132","https://openalex.org/W1970185852","https://openalex.org/W1970585283","https://openalex.org/W1983354332","https://openalex.org/W1984827842","https://openalex.org/W2007395042","https://openalex.org/W2013183108","https://openalex.org/W2033424999","https://openalex.org/W2035765621","https://openalex.org/W2038281434","https://openalex.org/W2060259047","https://openalex.org/W2068484625","https://openalex.org/W2073664445","https://openalex.org/W2079440004","https://openalex.org/W2090963365","https://openalex.org/W2091127828","https://openalex.org/W2100514507","https://openalex.org/W2107501462","https://openalex.org/W2113642685","https://openalex.org/W2142053777","https://openalex.org/W2143476164","https://openalex.org/W2478091498","https://openalex.org/W2798909945","https://openalex.org/W2963389536","https://openalex.org/W2963649064","https://openalex.org/W3135227555","https://openalex.org/W3147626731"],"related_works":["https://openalex.org/W2147776645","https://openalex.org/W2122094047","https://openalex.org/W399006150","https://openalex.org/W2049306475","https://openalex.org/W4292324088","https://openalex.org/W2027835668","https://openalex.org/W2997140122","https://openalex.org/W4362700221","https://openalex.org/W2403877097","https://openalex.org/W2033206711"],"abstract_inverted_index":{"Anderson($m$)":[0,43],"is":[1,33,44,53],"a":[2,26,54],"method":[3],"for":[4,90],"acceleration":[5],"of":[6,15,29,74,80],"fixed":[7,17,34,50],"point":[8,18,35,51],"iteration":[9,24],"which":[10,106],"stores":[11],"m+1":[12],"prior":[13],"evaluations":[14],"the":[16,22,49,57,60,68,78,87,91,108],"map":[19,52],"and":[20,56,96,101],"computes":[21],"new":[23],"as":[25],"linear":[27,61,81],"combination":[28,62],"those":[30],"evaluations.":[31],"Anderson(0)":[32],"iteration.":[36],"In":[37],"this":[38],"paper":[39],"we":[40,70],"show":[41],"that":[42,86],"locally":[45],"r-linearly":[46],"convergent":[47],"if":[48],"contraction":[55],"coefficients":[58,92],"in":[59,77,98],"remain":[63],"bounded.":[64],"Without":[65],"assumptions":[66],"on":[67,103],"coefficients,":[69],"prove":[71],"q-linear":[72],"convergence":[73],"Anderson(1)":[75],"and,":[76],"case":[79],"problems,":[82],"Anderson($m$).":[83],"We":[84],"observe":[85],"optimization":[88],"problem":[89],"can":[93],"be":[94],"formulated":[95],"solved":[97],"nonstandard":[99],"ways":[100],"report":[102],"numerical":[104],"experiments":[105],"illustrate":[107],"ideas.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":23},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":32},{"year":2020,"cited_by_count":36},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}