{"id":"https://openalex.org/W2117673385","doi":"https://doi.org/10.1002/nla.1680010306","title":"Improved SSOR and incomplete Cholesky solution of linear equations on shared memory and distributed memory parallel computers","display_name":"Improved SSOR and incomplete Cholesky solution of linear equations on shared memory and distributed memory parallel computers","publication_year":1994,"publication_date":"1994-05-01","ids":{"openalex":"https://openalex.org/W2117673385","doi":"https://doi.org/10.1002/nla.1680010306","mag":"2117673385"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1680010306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680010306","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","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/A5062940770","display_name":"Wayne Joubert","orcid":"https://orcid.org/0000-0003-4771-998X"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wayne Joubert","raw_affiliation_strings":["Computer Research and Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"affiliations":[{"raw_affiliation_string":"Computer Research and Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007589413","display_name":"Thomas C. Oppe","orcid":null},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Oppe","raw_affiliation_strings":["Supercomputer Computations and Research Institute, Florida State University, Tallahassee, FL 32306, USA"],"affiliations":[{"raw_affiliation_string":"Supercomputer Computations and Research Institute, Florida State University, Tallahassee, FL 32306, USA","institution_ids":["https://openalex.org/I103163165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062940770"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.22816901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"1","issue":"3","first_page":"287","last_page":"311"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9969000220298767,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9947999715805054,"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.8973509073257446},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.776339054107666},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.6575579643249512},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6261094212532043},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.6210371255874634},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.6142082810401917},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5066119432449341},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.350774884223938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33386433124542236}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.8973509073257446},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.776339054107666},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.6575579643249512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6261094212532043},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.6210371255874634},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.6142082810401917},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5066119432449341},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.350774884223938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33386433124542236},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nla.1680010306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680010306","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","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":22,"referenced_works":["https://openalex.org/W123575845","https://openalex.org/W177599668","https://openalex.org/W1516307186","https://openalex.org/W1538510001","https://openalex.org/W1590879322","https://openalex.org/W1982919029","https://openalex.org/W1992208469","https://openalex.org/W2000250112","https://openalex.org/W2005040897","https://openalex.org/W2048255281","https://openalex.org/W2066637873","https://openalex.org/W2076485756","https://openalex.org/W2083149327","https://openalex.org/W2087046932","https://openalex.org/W2170928089","https://openalex.org/W2288887139","https://openalex.org/W2316564661","https://openalex.org/W2325556328","https://openalex.org/W2588081979","https://openalex.org/W4247600657","https://openalex.org/W4299343067","https://openalex.org/W4300938688"],"related_works":["https://openalex.org/W2078637543","https://openalex.org/W2986384163","https://openalex.org/W3022256543","https://openalex.org/W898189783","https://openalex.org/W4234447426","https://openalex.org/W1977632218","https://openalex.org/W4367461038","https://openalex.org/W1598598610","https://openalex.org/W4300806383","https://openalex.org/W2066284316"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"two":[4],"new":[5,25,72],"implementations":[6,26,121],"of":[7,46,59,81,111,119],"SSOR":[8],"and":[9,18,88,124,138],"incomplete":[10],"factorization":[11],"preconditioners":[12,61],"are":[13,122,127],"given,":[14,123],"for":[15,31,50,129],"shared":[16,68],"memory":[17,20,69,96],"distributed":[19,95],"parallel":[21,92],"computers":[22],"respectively.":[23],"These":[24],"give":[27],"increased":[28],"solution":[29],"speeds":[30],"matrix":[32],"problems":[33],"such":[34],"as":[35],"those":[36],"arising":[37],"from":[38],"discretized":[39],"partial":[40],"differential":[41],"equations":[42],"with":[43],"natural":[44],"ordering":[45],"the":[47,56,79,109,115,120,135,139],"grid":[48],"points,":[49],"which":[51,77,107],"it":[52],"is":[53,62,74,105],"well\u2010known":[54],"that":[55],"standard":[57],"implementation":[58,99],"these":[60],"difficult":[63],"to":[64],"parallelize":[65],"effectively.":[66],"For":[67,94],"machines,":[70,97],"a":[71,130],"technique":[73],"presented":[75],"here":[76],"decreases":[78],"number":[80],"synchronization":[82],"points":[83],"in":[84],"each":[85],"preconditioning":[86,116],"step":[87],"thus":[89],"allows":[90],"better":[91],"speedups.":[93],"an":[98],"based":[100],"on":[101,134],"block":[102],"cyclic":[103],"reduction":[104],"given":[106,128],"circumvents":[108],"problem":[110,133],"idle":[112],"processors":[113],"during":[114],"phase.":[117],"Descriptions":[118],"numerical":[125],"comparisons":[126],"model":[131],"diffusion":[132],"Cray":[136],"Y\u2010MP":[137],"CM\u20102":[140],"Connection":[141],"Machine.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
