{"id":"https://openalex.org/W2473876198","doi":"https://doi.org/10.1137/15m1028534","title":"An Adaptive MultiPreconditioned Conjugate Gradient Algorithm","display_name":"An Adaptive MultiPreconditioned Conjugate Gradient Algorithm","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2473876198","doi":"https://doi.org/10.1137/15m1028534","mag":"2473876198"},"language":"en","primary_location":{"id":"doi:10.1137/15m1028534","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1028534","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5076520272","display_name":"Nicole Spillane","orcid":"https://orcid.org/0000-0001-5067-946X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nicole Spillane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076520272"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3259,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94574668,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"A1896","last_page":"A1918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8370000123977661,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8370000123977661,"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":0.11969999969005585,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.010599999688565731,"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/preconditioner","display_name":"Preconditioner","score":0.9600928425788879},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8727535009384155},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.786774754524231},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5827978253364563},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5707682967185974},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5668574571609497},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5523055791854858},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.5185883045196533},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5027804374694824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4877491593360901},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4872497618198395},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.48220646381378174},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4593842625617981},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4556671679019928},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3874610364437103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36348074674606323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19825875759124756},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14616551995277405},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.1177855134010315},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11347824335098267}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9600928425788879},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8727535009384155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.786774754524231},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5827978253364563},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5707682967185974},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5668574571609497},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5523055791854858},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.5185883045196533},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5027804374694824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4877491593360901},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4872497618198395},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.48220646381378174},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4593842625617981},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4556671679019928},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3874610364437103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36348074674606323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19825875759124756},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14616551995277405},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.1177855134010315},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11347824335098267},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1028534","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1028534","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7568617334","display_name":null,"funder_award_id":"Fondecyt 3150090","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"}],"funders":[{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1932034027","https://openalex.org/W1968250174","https://openalex.org/W1974521166","https://openalex.org/W1987710178","https://openalex.org/W1991532854","https://openalex.org/W1992110290","https://openalex.org/W1993993976","https://openalex.org/W2000867371","https://openalex.org/W2005390260","https://openalex.org/W2012728721","https://openalex.org/W2018190542","https://openalex.org/W2028975965","https://openalex.org/W2028989647","https://openalex.org/W2030373618","https://openalex.org/W2033286780","https://openalex.org/W2039980550","https://openalex.org/W2040425799","https://openalex.org/W2043368701","https://openalex.org/W2057141432","https://openalex.org/W2058751009","https://openalex.org/W2061813658","https://openalex.org/W2062446082","https://openalex.org/W2070232376","https://openalex.org/W2082804737","https://openalex.org/W2083059396","https://openalex.org/W2103706435","https://openalex.org/W2105293202","https://openalex.org/W2108533624","https://openalex.org/W2114535880","https://openalex.org/W2124087857","https://openalex.org/W2135167588","https://openalex.org/W2139172930","https://openalex.org/W2200128022","https://openalex.org/W2316564661","https://openalex.org/W2912759508","https://openalex.org/W2963631308","https://openalex.org/W3098036980","https://openalex.org/W3124201142","https://openalex.org/W4235024121","https://openalex.org/W4242493951"],"related_works":["https://openalex.org/W4229577910","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2026707481","https://openalex.org/W2353110519","https://openalex.org/W2743060302","https://openalex.org/W2117656216","https://openalex.org/W3194092090","https://openalex.org/W2159515580","https://openalex.org/W2106898404"],"abstract_inverted_index":{"This":[0,81],"article":[1],"introduces":[2],"and":[3,119,141],"analyzes":[4],"a":[5,28,44,58,96,148,153],"new":[6,33],"adaptive":[7],"algorithm":[8,110],"for":[9,98,138],"solving":[10],"symmetric":[11],"positive":[12],"definite":[13],"linear":[14,156],"systems":[15],"in":[16,85,133],"cases":[17],"where":[18],"several":[19],"preconditioners":[20],"are":[21],"available":[22],"or":[23,66],"the":[24,54,90,99,103,109,114],"usual":[25],"preconditioner":[26],"is":[27,51,82,106,111,122,128],"sum":[29],"of":[30,60,77,102,135],"contributions.":[31],"A":[32],"theoretical":[34],"result":[35],"allows":[36],"us":[37],"to":[38,70,113,130,151],"select,":[39],"at":[40,61],"each":[41],"iteration,":[42],"whether":[43,67],"classical":[45],"preconditioned":[46,104],"conjugate":[47],"gradient":[48],"(CG)":[49],"iteration":[50,76],"sufficient":[52],"(i.e.,":[53],"error":[55],"decreases":[56],"by":[57,73],"factor":[59],"least":[62],"some":[63],"chosen":[64],"ratio)":[65],"convergence":[68],"needs":[69],"be":[71,131,152],"accelerated":[72],"performing":[74],"an":[75,86],"multipreconditioned":[78],"CG":[79],"[4].":[80],"first":[83],"presented":[84],"abstract":[87],"framework":[88],"with":[89],"one":[91],"strong":[92],"assumption":[93],"being":[94],"that":[95],"bound":[97],"smallest":[100],"eigenvalue":[101],"operator":[105],"available.":[107],"Then,":[108],"applied":[112],"balancing":[115],"domain":[116],"decomposition":[117],"method":[118],"its":[120],"behavior":[121],"illustrated":[123],"numerically.":[124],"In":[125],"particular,":[126],"it":[127,147],"observed":[129],"optimal":[132],"terms":[134],"local":[136],"solves,":[137],"both":[139],"well-conditioned":[140],"ill-conditioned":[142],"test":[143],"cases,":[144],"which":[145],"makes":[146],"good":[149],"candidate":[150],"default":[154],"parallel":[155],"solver.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-30T09:04:40.226872","created_date":"2025-10-10T00:00:00"}