{"id":"https://openalex.org/W2019527978","doi":"https://doi.org/10.1137/090757216","title":"Design of a Multicore Sparse Cholesky Factorization Using DAGs","display_name":"Design of a Multicore Sparse Cholesky Factorization Using DAGs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2019527978","doi":"https://doi.org/10.1137/090757216","mag":"2019527978"},"language":"en","primary_location":{"id":"doi:10.1137/090757216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757216","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/A5008888668","display_name":"Jonathan Hogg","orcid":"https://orcid.org/0000-0001-6372-4880"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. D. Hogg","raw_affiliation_strings":["jonathan.hogg@stfc.ac.uk and john.reid@stfc.ac.uk and jennifer.scott@stfc.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jonathan.hogg@stfc.ac.uk and john.reid@stfc.ac.uk and jennifer.scott@stfc.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081863886","display_name":"John Reid","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. K. Reid","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057481528","display_name":"J. A. Scott","orcid":"https://orcid.org/0000-0003-2130-1091"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. A. Scott","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5417,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.94559219,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"32","issue":"6","first_page":"3627","last_page":"3649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.9170694351196289},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.738290548324585},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.6797764301300049},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.641977071762085},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6120365858078003},{"id":"https://openalex.org/keywords/multi-core-processor","display_name":"Multi-core processor","score":0.5112345218658447},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.42870235443115234},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.41591113805770874},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.415299654006958},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3133188486099243},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1392555832862854}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9170694351196289},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.738290548324585},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.6797764301300049},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.641977071762085},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6120365858078003},{"id":"https://openalex.org/C78766204","wikidata":"https://www.wikidata.org/wiki/Q555032","display_name":"Multi-core processor","level":2,"score":0.5112345218658447},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.42870235443115234},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.41591113805770874},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.415299654006958},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3133188486099243},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1392555832862854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090757216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757216","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:epubs.cclrc.ac.uk:work/51895","is_oa":false,"landing_page_url":"http://purl.org/net/epubs/work/51895","pdf_url":null,"source":{"id":"https://openalex.org/S4306400600","display_name":"ePubs (Science and Technology Facilities Council, Research Councils UK)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162524378","host_organization_name":"Science and Technology Facilities Council","host_organization_lineage":["https://openalex.org/I162524378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"},{"id":"pmh:oai:purl.org/net/epubs:work/49215922","is_oa":false,"landing_page_url":"http://purl.org/net/epubs/work/49215922","pdf_url":null,"source":{"id":"https://openalex.org/S4306400334","display_name":"Science and Technology Facilities Council","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162524378","host_organization_name":"Science and Technology Facilities Council","host_organization_lineage":["https://openalex.org/I162524378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G6222400635","display_name":null,"funder_award_id":"EP/F006535/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7278630660","display_name":null,"funder_award_id":"EP/E053351/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1486196049","https://openalex.org/W1536852470","https://openalex.org/W1583920484","https://openalex.org/W1584866192","https://openalex.org/W1842923156","https://openalex.org/W1890479029","https://openalex.org/W1970009422","https://openalex.org/W1988457600","https://openalex.org/W1992935334","https://openalex.org/W1993274656","https://openalex.org/W2003105834","https://openalex.org/W2013424510","https://openalex.org/W2013459285","https://openalex.org/W2016279572","https://openalex.org/W2032401773","https://openalex.org/W2033624514","https://openalex.org/W2034036349","https://openalex.org/W2051917325","https://openalex.org/W2052602889","https://openalex.org/W2053427525","https://openalex.org/W2055094346","https://openalex.org/W2063675347","https://openalex.org/W2070232376","https://openalex.org/W2070299075","https://openalex.org/W2088501249","https://openalex.org/W2089024363","https://openalex.org/W2094542090","https://openalex.org/W2096541795","https://openalex.org/W2113277707","https://openalex.org/W2113533974","https://openalex.org/W2117266970","https://openalex.org/W2124480634","https://openalex.org/W2127009405","https://openalex.org/W2353286494"],"related_works":["https://openalex.org/W1509943448","https://openalex.org/W2526784484","https://openalex.org/W1987177655","https://openalex.org/W4318710973","https://openalex.org/W2127144731","https://openalex.org/W253708524","https://openalex.org/W2025695688","https://openalex.org/W232494833","https://openalex.org/W2074431240","https://openalex.org/W2100843445"],"abstract_inverted_index":{"The":[0,105],"rapid":[1],"emergence":[2],"of":[3,26,42,55,101,155,166,209],"multicore":[4],"machines":[5],"has":[6],"led":[7],"to":[8,11,59],"the":[9,24,39,43,46,62,87,92,102,156,207],"need":[10],"design":[12,175],"new":[13,136],"algorithms":[14],"that":[15,64,172,179,201],"are":[16,122,193],"efficient":[17,137],"on":[18,51,86,99,187],"these":[19,68,108],"architectures.":[20],"Here,":[21],"we":[22,168],"consider":[23],"solution":[25],"sparse":[27,82],"symmetric":[28],"positive-definite":[29],"linear":[30],"systems":[31],"by":[32,38,75,114],"Cholesky":[33,103],"factorization.":[34],"We":[35],"were":[36],"motivated":[37],"successful":[40],"division":[41],"computation":[44],"in":[45,145,206],"dense":[47],"case":[48,208],"into":[49,97],"tasks":[50,98,109],"blocks":[52,100,121],"and":[53,90,138,150,177,184,199],"use":[54],"a":[56,76,115,135,164],"task":[57],"manager":[58],"exploit":[60],"all":[61],"parallelism":[63],"is":[65,84,132,143,151],"available":[66,152],"between":[67,107],"tasks,":[69],"whose":[70],"dependencies":[71,106],"may":[72,110],"be":[73,112],"represented":[74,113],"directed":[77],"acyclic":[78],"graph":[79],"(DAG).":[80],"Our":[81,130],"algorithm":[83,131],"built":[85],"assembly":[88],"tree":[89],"subdivides":[91],"work":[93],"at":[94],"each":[95],"node":[96],"factor.":[104],"again":[111],"DAG.":[116],"To":[117],"limit":[118],"memory":[119],"requirements,":[120],"updated":[123],"directly":[124],"rather":[125],"than":[126],"through":[127],"generated-element":[128],"matrices.":[129],"implemented":[133],"within":[134],"portable":[139],"solver":[140],"HSL_MA87.":[141],"It":[142],"written":[144],"Fortran":[146],"95":[147],"plus":[148],"OpenMP":[149],"as":[153],"part":[154],"software":[157],"library":[158],"HSL.":[159],"Using":[160],"problems":[161],"arising":[162],"from":[163],"range":[165],"applications,":[167],"present":[169],"experimental":[170],"results":[171],"support":[173],"our":[174,188],"choices":[176],"demonstrate":[178],"HSL_MA87":[180,202],"obtains":[181],"good":[182],"serial":[183],"parallel":[185],"times":[186],"8-core":[189],"test":[190],"machines.":[191],"Comparisons":[192],"made":[194],"with":[195],"existing":[196],"modern":[197],"solvers":[198],"show":[200],"performs":[203],"well,":[204],"particularly":[205],"very":[210],"large":[211],"problems.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":29},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2016-06-24T00:00:00"}
