{"id":"https://openalex.org/W4381712570","doi":"https://doi.org/10.3390/a16050242","title":"Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors","display_name":"Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors","publication_year":2023,"publication_date":"2023-05-07","ids":{"openalex":"https://openalex.org/W4381712570","doi":"https://doi.org/10.3390/a16050242"},"language":"en","primary_location":{"id":"doi:10.3390/a16050242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16050242","pdf_url":"https://www.mdpi.com/1999-4893/16/5/242/pdf?version=1684739542","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/5/242/pdf?version=1684739542","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047991343","display_name":"D. V. Lukyanenko","orcid":"https://orcid.org/0000-0001-5140-3617"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Dmitry Lukyanenko","raw_affiliation_strings":["Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047991343"],"corresponding_institution_ids":["https://openalex.org/I19880235"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.6644,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.95388943,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"16","issue":"5","first_page":"242","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T14470","display_name":"Advanced Data Processing Techniques","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T13608","display_name":"Advanced Computational Techniques in Science and Engineering","score":0.9689000248908997,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/overdetermined-system","display_name":"Overdetermined system","score":0.8655170202255249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7550859451293945},{"id":"https://openalex.org/keywords/python","display_name":"Python (programming language)","score":0.6363054513931274},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5882182121276855},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5417935848236084},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49691417813301086},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.47424688935279846},{"id":"https://openalex.org/keywords/message-passing-interface","display_name":"Message Passing Interface","score":0.4364425837993622},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4142223000526428},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4141598343849182},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.37237459421157837},{"id":"https://openalex.org/keywords/message-passing","display_name":"Message passing","score":0.27114352583885193},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.26423007249832153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21397343277931213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.13722345232963562}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.8655170202255249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7550859451293945},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.6363054513931274},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5882182121276855},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5417935848236084},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49691417813301086},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.47424688935279846},{"id":"https://openalex.org/C166782233","wikidata":"https://www.wikidata.org/wiki/Q127879","display_name":"Message Passing Interface","level":3,"score":0.4364425837993622},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4142223000526428},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4141598343849182},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.37237459421157837},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.27114352583885193},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.26423007249832153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21397343277931213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.13722345232963562},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a16050242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16050242","pdf_url":"https://www.mdpi.com/1999-4893/16/5/242/pdf?version=1684739542","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:aad849cd1aee448f9c0b1eb9e7be8ca9","is_oa":true,"landing_page_url":"https://doaj.org/article/aad849cd1aee448f9c0b1eb9e7be8ca9","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 16, Iss 5, p 242 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/16/5/242/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a16050242","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 16; Issue 5; Pages: 242","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a16050242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16050242","pdf_url":"https://www.mdpi.com/1999-4893/16/5/242/pdf?version=1684739542","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5600000023841858}],"awards":[{"id":"https://openalex.org/G7247445720","display_name":null,"funder_award_id":"23-41-00002","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"},{"id":"https://openalex.org/F4320329591","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4381712570.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W72753083","https://openalex.org/W1507702133","https://openalex.org/W1552224009","https://openalex.org/W1980677368","https://openalex.org/W1982059058","https://openalex.org/W1983961353","https://openalex.org/W2074190947","https://openalex.org/W2082479178","https://openalex.org/W2083027300","https://openalex.org/W2093259859","https://openalex.org/W2105293202","https://openalex.org/W2117221287","https://openalex.org/W2119404459","https://openalex.org/W2121402967","https://openalex.org/W2170198330","https://openalex.org/W2303004438","https://openalex.org/W2316564661","https://openalex.org/W2736042498","https://openalex.org/W2760051565","https://openalex.org/W2897248362","https://openalex.org/W2945682103","https://openalex.org/W2964082713","https://openalex.org/W2964301053","https://openalex.org/W3179991146","https://openalex.org/W4205624883","https://openalex.org/W4236873655","https://openalex.org/W4247363778","https://openalex.org/W4295549063","https://openalex.org/W4298293704"],"related_works":["https://openalex.org/W4386576538","https://openalex.org/W60923334","https://openalex.org/W2125322432","https://openalex.org/W4382519919","https://openalex.org/W1981326443","https://openalex.org/W2063945179","https://openalex.org/W134667518","https://openalex.org/W2087304636","https://openalex.org/W4224254018","https://openalex.org/W1988771669"],"abstract_inverted_index":{"The":[0,55,91,125],"paper":[1],"proposes":[2],"a":[3,16,27,48,62,112],"parallel":[4,56,77],"algorithm":[5,20,57],"for":[6,83],"solving":[7],"large":[8],"overdetermined":[9],"systems":[10],"of":[11,26,29,71,87,127],"linear":[12],"algebraic":[13],"equations":[14],"with":[15],"dense":[17],"matrix.":[18],"This":[19],"is":[21,35,58,81,133],"based":[22],"on":[23],"the":[24,30,52,69,72,84,88,97,102,121,129],"use":[25],"modification":[28],"conjugate":[31],"gradient":[32],"method,":[33],"which":[34,80],"able":[36],"to":[37,50],"take":[38],"into":[39,67],"account":[40,68],"rounding":[41],"errors":[42],"accumulated":[43],"during":[44],"calculations":[45],"when":[46],"making":[47],"decision":[49],"terminate":[51],"iterative":[53],"process.":[54],"constructed":[59],"in":[60,110],"such":[61,111],"way":[63,113],"that":[64,114],"it":[65],"takes":[66],"capabilities":[70],"message":[73],"passing":[74],"interface":[75],"(MPI)":[76],"programming":[78,92,99,123],"technology,":[79],"used":[82],"software":[85],"implementation":[86],"proposed":[89],"algorithm.":[90],"examples":[93],"are":[94,108],"shown":[95],"using":[96,120,128],"Python":[98],"language":[100],"and":[101],"mpi4py":[103],"package,":[104],"but":[105],"all":[106],"programs":[107],"built":[109],"they":[115],"can":[116],"be":[117],"easily":[118],"rewritten":[119],"C/C++/Fortran":[122],"languages.":[124],"advantage":[126],"modern":[130],"MPI-4.0":[131],"standard":[132],"demonstrated.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
