{"id":"https://openalex.org/W1834710643","doi":"https://doi.org/10.1109/tc.1977.1674932","title":"Iterative Solution of Linear Equations on a Parallel Processor System","display_name":"Iterative Solution of Linear Equations on a Parallel Processor System","publication_year":1977,"publication_date":"1977-09-01","ids":{"openalex":"https://openalex.org/W1834710643","doi":"https://doi.org/10.1109/tc.1977.1674932","mag":"1834710643"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1977.1674932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1977.1674932","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":"https://openalex.org/A5082071791","display_name":"Conrad","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"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Conrad","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology","Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","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"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Wallach","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.1078,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9732334,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"C-26","issue":"9","first_page":"838","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9776999950408936,"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"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9776999950408936,"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9599999785423279,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9169999957084656,"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/computer-science","display_name":"Computer science","score":0.7050377130508423},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6847333908081055},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6676366925239563},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6668752431869507},{"id":"https://openalex.org/keywords/jacobi-method","display_name":"Jacobi method","score":0.6429786682128906},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.637282133102417},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5898130536079407},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5471996665000916},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.5395715832710266},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.5257300138473511},{"id":"https://openalex.org/keywords/parallel-processing","display_name":"Parallel processing","score":0.5210306644439697},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.5007319450378418},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42972850799560547},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36668166518211365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22504451870918274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20575621724128723}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7050377130508423},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6847333908081055},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6676366925239563},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6668752431869507},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.6429786682128906},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.637282133102417},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5898130536079407},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5471996665000916},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.5395715832710266},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.5257300138473511},{"id":"https://openalex.org/C106515295","wikidata":"https://www.wikidata.org/wiki/Q26806595","display_name":"Parallel processing","level":2,"score":0.5210306644439697},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.5007319450378418},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42972850799560547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36668166518211365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22504451870918274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20575621724128723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1977.1674932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1977.1674932","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":[{"id":"https://metadata.un.org/sdg/4","score":0.8100000023841858,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W6625533","https://openalex.org/W120254435","https://openalex.org/W1530081230","https://openalex.org/W1855301476","https://openalex.org/W1979933194","https://openalex.org/W2025786274","https://openalex.org/W2030121615","https://openalex.org/W2046266069","https://openalex.org/W2065680376","https://openalex.org/W2132877409","https://openalex.org/W2321653420"],"related_works":["https://openalex.org/W3097974237","https://openalex.org/W2389138357","https://openalex.org/W3131955914","https://openalex.org/W2433204144","https://openalex.org/W3198846263","https://openalex.org/W2358921742","https://openalex.org/W2964360302","https://openalex.org/W4382519917","https://openalex.org/W3184983074","https://openalex.org/W2074512878"],"abstract_inverted_index":{"A":[0,11,67],"parallel":[1,51,94],"processor":[2,95],"system":[3],"and":[4,38,62],"its":[5],"mode":[6],"of":[7,24,27,36,47,57,69],"operation":[8],"are":[9,30,40,60],"described.":[10],"notation":[12],"for":[13,21,53,73],"writing":[14],"programs":[15],"on":[16,92],"it":[17],"is":[18,65,71],"introduced.":[19],"Methods":[20],"iterative":[22,55],"solution":[23,56],"a":[25,93],"set":[26],"linear":[28,58],"equations":[29,59],"then":[31],"discussed.":[32,66],"The":[33],"well-known":[34],"algorithms":[35,83],"Jacobi":[37],"Gauss\u2013Seidel":[39],"parallelized":[41],"despite":[42],"the":[43,48,54,82,86],"apparent":[44],"inherent":[45],"sequentiality":[46],"latter.":[49],"New,":[50],"methods":[52],"introduced":[61],"their":[63],"convergence":[64],"measure":[68],"speedup":[70],"computed":[72],"all":[74],"methods.":[75],"It":[76],"shows":[77],"that":[78],"in":[79,85],"most":[80],"cases":[81],"developed":[84],"paper":[87],"may":[88],"be":[89],"efficiently":[90],"executed":[91],"system.":[96]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}