{"id":"https://openalex.org/W2041994515","doi":"https://doi.org/10.1109/tc.1980.1675585","title":"On Block-Parallel Methods for Solving Linear Equations","display_name":"On Block-Parallel Methods for Solving Linear Equations","publication_year":1980,"publication_date":"1980-05-01","ids":{"openalex":"https://openalex.org/W2041994515","doi":"https://doi.org/10.1109/tc.1980.1675585","mag":"2041994515"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1980.1675585","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675585","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","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":null,"display_name":"Wallach","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Wallach","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","Department of Electrical Engineering, Wayne State University, Detroit, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Electrical Engineering, Wayne State University, Detroit, MI, USA","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105998696","display_name":"Konrad","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Konrad","raw_affiliation_strings":["Division of Computer Science, University of California, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Computer Science, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2005,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.98389831,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"C-29","issue":"5","first_page":"354","last_page":"359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.977400004863739,"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":0.977400004863739,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9276999831199646,"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":0.9061999917030334,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.8631969094276428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7439350485801697},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.7063639163970947},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6975089311599731},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.6478297710418701},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5320706367492676},{"id":"https://openalex.org/keywords/parallel-processing","display_name":"Parallel processing","score":0.49739888310432434},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4798566699028015},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4499354362487793},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.43497782945632935},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.41492849588394165},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40291327238082886},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.28772538900375366},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.23102274537086487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20578160881996155},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1467137634754181}],"concepts":[{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.8631969094276428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7439350485801697},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.7063639163970947},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6975089311599731},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.6478297710418701},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5320706367492676},{"id":"https://openalex.org/C106515295","wikidata":"https://www.wikidata.org/wiki/Q26806595","display_name":"Parallel processing","level":2,"score":0.49739888310432434},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4798566699028015},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4499354362487793},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.43497782945632935},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.41492849588394165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40291327238082886},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28772538900375366},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.23102274537086487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20578160881996155},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1467137634754181},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1980.1675585","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675585","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1834710643","https://openalex.org/W1995282402","https://openalex.org/W2009377158","https://openalex.org/W2046266069","https://openalex.org/W2083007549","https://openalex.org/W2091323284","https://openalex.org/W2095415247"],"related_works":["https://openalex.org/W2011913132","https://openalex.org/W1527081774","https://openalex.org/W2511738012","https://openalex.org/W2047893452","https://openalex.org/W2044608416","https://openalex.org/W2004058992","https://openalex.org/W2491524947","https://openalex.org/W3198846263","https://openalex.org/W2205038830","https://openalex.org/W4382519917"],"abstract_inverted_index":{"An":[0],"MIMD-type":[1],"parallel-processing":[2],"system":[3],"was":[4],"introduced":[5],"recently.":[6],"Using":[7],"an":[8],"extended":[9],"PL/I":[10],"notation,":[11],"algorithms":[12],"for":[13,18,23],"the":[14],"Gauss-Seidel":[15],"method":[16],"and":[17],"back":[19],"substitution":[20],"are":[21],"written":[22],"this":[24],"system.":[25],"Block":[26],"execution":[27],"is":[28],"shown":[29],"to":[30],"result":[31],"in":[32],"higher":[33],"speedups.":[34]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}