{"id":"https://openalex.org/W2014492721","doi":"https://doi.org/10.1137/080717481","title":"Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems","display_name":"Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2014492721","doi":"https://doi.org/10.1137/080717481","mag":"2014492721"},"language":"en","primary_location":{"id":"doi:10.1137/080717481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717481","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/A5060981469","display_name":"Tarek P. Mathew","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tarek P. Mathew","raw_affiliation_strings":["tmathew@poonithara.org#TAB#"],"affiliations":[{"raw_affiliation_string":"tmathew@poonithara.org#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025777901","display_name":"Marcus Sarkis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcus Sarkis","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043172751","display_name":"Christian E. Schaerer","orcid":"https://orcid.org/0000-0002-0587-7704"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Christian E. Schaerer","raw_affiliation_strings":["cschaer@impa.br and cschaer@pol.una.py#TAB#"],"affiliations":[{"raw_affiliation_string":"cschaer@impa.br and cschaer@pol.una.py#TAB#","institution_ids":["https://openalex.org/I141883831"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060981469"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7161,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.83998892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"3","first_page":"1180","last_page":"1200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9608451128005981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7796890735626221},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7254524230957031},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6736897826194763},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5568670034408569},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.540638267993927},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5351596474647522},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5152912139892578},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4611049294471741},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4585750699043274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45213738083839417},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4514535665512085},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.23596355319023132},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17142704129219055}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9608451128005981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7796890735626221},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7254524230957031},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6736897826194763},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5568670034408569},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.540638267993927},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5351596474647522},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5152912139892578},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4611049294471741},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4585750699043274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45213738083839417},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4514535665512085},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23596355319023132},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17142704129219055},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080717481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717481","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"},{"id":"pmh:oai:digitalcommons.wpi.edu:mathematicalsciences-pubs-1038","is_oa":false,"landing_page_url":"https://digitalcommons.wpi.edu/mathematicalsciences-pubs/38","pdf_url":null,"source":{"id":"https://openalex.org/S4377196141","display_name":"Digital WPI","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Sciences Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W52326106","https://openalex.org/W168475654","https://openalex.org/W1528030462","https://openalex.org/W1760551737","https://openalex.org/W1764732869","https://openalex.org/W1976685335","https://openalex.org/W1979475531","https://openalex.org/W1984840642","https://openalex.org/W1999331305","https://openalex.org/W2010530933","https://openalex.org/W2022977680","https://openalex.org/W2027491117","https://openalex.org/W2055116131","https://openalex.org/W2059262502","https://openalex.org/W2068696746","https://openalex.org/W2080621333","https://openalex.org/W2094411006","https://openalex.org/W2105970221","https://openalex.org/W2126906098","https://openalex.org/W2140489561","https://openalex.org/W2141870784","https://openalex.org/W2170359064","https://openalex.org/W2238405919","https://openalex.org/W3035235874"],"related_works":["https://openalex.org/W3160810049","https://openalex.org/W1482750774","https://openalex.org/W2986665254","https://openalex.org/W1994349276","https://openalex.org/W3204470723","https://openalex.org/W4285325102","https://openalex.org/W1575783825","https://openalex.org/W2096346341","https://openalex.org/W2525981419","https://openalex.org/W2104711345"],"abstract_inverted_index":{"In":[0],"this":[1,106],"paper,":[2],"we":[3],"describe":[4],"block":[5,96],"matrix":[6],"algorithms":[7,131],"for":[8],"the":[9,38,61,74,102,110,113,122,129,142],"iterative":[10,43],"solution":[11],"of":[12,37,105],"a":[13,20,26,52,88,93,117],"large-scale":[14],"linear-quadratic":[15],"optimal":[16,133],"control":[17,28,63],"problem":[18,39],"involving":[19,59],"parabolic":[21],"partial":[22],"differential":[23],"equation":[24],"over":[25],"finite":[27],"horizon.":[29],"We":[30],"consider":[31],"an":[32,83],"\u201call":[33],"at":[34],"once\u201d":[35],"discretization":[36],"and":[40,136],"formulate":[41],"three":[42],"algorithms.":[44],"The":[45,70,98],"first":[46,75],"algorithm":[47,72,76,100,115],"is":[48,101],"based":[49,120],"on":[50,121],"preconditioning":[51],"symmetric":[53,89],"positive":[54,94],"definite":[55,95],"reduced":[56],"linear":[57],"system":[58,91],"only":[60],"unknown":[62],"variables;":[64],"however":[65],"inner-outer":[66,79],"iterations":[67,80],"are":[68],"required.":[69],"second":[71,114],"modifies":[73,109],"to":[77],"avoid":[78],"by":[81,116],"introducing":[82],"auxiliary":[84],"variable.":[85],"It":[86,108],"yields":[87],"indefinite":[90],"with":[92],"preconditioner.":[97],"third":[99],"central":[103],"focus":[104],"paper.":[107],"preconditioner":[111,119],"in":[112],"parallel-in-time":[118],"parareal":[123],"algorithm.":[124],"Theoretical":[125],"results":[126],"show":[127],"that":[128],"preconditioned":[130],"have":[132],"convergence":[134],"properties":[135],"parallel":[137],"scalability.":[138],"Numerical":[139],"experiments":[140],"confirm":[141],"theoretical":[143],"results.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}