{"id":"https://openalex.org/W1964962098","doi":"https://doi.org/10.1137/080734716","title":"John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis","display_name":"John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1964962098","doi":"https://doi.org/10.1137/080734716","mag":"1964962098"},"language":"en","primary_location":{"id":"doi:10.1137/080734716","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734716","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5011692821","display_name":"Joseph F. Grcar","orcid":null},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joseph F. Grcar","raw_affiliation_strings":["jfgrcar@comcast.net and na.grcar@na-net. ornl.gov#TAB#"],"affiliations":[{"raw_affiliation_string":"jfgrcar@comcast.net and na.grcar@na-net. ornl.gov#TAB#","institution_ids":["https://openalex.org/I1289243028"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011692821"],"corresponding_institution_ids":["https://openalex.org/I1289243028"],"apc_list":null,"apc_paid":null,"fwci":4.5239,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.94725677,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"4","first_page":"607","last_page":"682"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9945999979972839,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9945999979972839,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.9213494658470154},{"id":"https://openalex.org/keywords/futures-studies","display_name":"Futures studies","score":0.635842502117157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49395567178726196},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4900015890598297},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.4896448254585266},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4074874520301819},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3980942666530609},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34563225507736206},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3445793390274048},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3132621943950653},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2044924795627594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20057770609855652},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09162700176239014},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0886700451374054}],"concepts":[{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.9213494658470154},{"id":"https://openalex.org/C64848388","wikidata":"https://www.wikidata.org/wiki/Q188867","display_name":"Futures studies","level":2,"score":0.635842502117157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49395567178726196},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4900015890598297},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.4896448254585266},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4074874520301819},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3980942666530609},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34563225507736206},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3445793390274048},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3132621943950653},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2044924795627594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20057770609855652},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09162700176239014},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0886700451374054},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080734716","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734716","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.366.375","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe.tu-freiberg.de/~ernst/Lehre/Grundkurs/Literatur/grcar2011.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":233,"referenced_works":["https://openalex.org/W29988992","https://openalex.org/W45336737","https://openalex.org/W45779563","https://openalex.org/W50160758","https://openalex.org/W116806255","https://openalex.org/W121866904","https://openalex.org/W149522324","https://openalex.org/W159440238","https://openalex.org/W199984528","https://openalex.org/W323985845","https://openalex.org/W358598360","https://openalex.org/W381842933","https://openalex.org/W602774872","https://openalex.org/W615592791","https://openalex.org/W636282897","https://openalex.org/W650132556","https://openalex.org/W656555302","https://openalex.org/W657536329","https://openalex.org/W658559791","https://openalex.org/W846582679","https://openalex.org/W997348634","https://openalex.org/W1483691064","https://openalex.org/W1483820693","https://openalex.org/W1488731834","https://openalex.org/W1490170747","https://openalex.org/W1491339120","https://openalex.org/W1496427046","https://openalex.org/W1501224804","https://openalex.org/W1512567677","https://openalex.org/W1516226708","https://openalex.org/W1527571715","https://openalex.org/W1538356049","https://openalex.org/W1544013721","https://openalex.org/W1546750589","https://openalex.org/W1551831724","https://openalex.org/W1552212403","https://openalex.org/W1564377203","https://openalex.org/W1571722278","https://openalex.org/W1582284382","https://openalex.org/W1583388113","https://openalex.org/W1585380779","https://openalex.org/W1602867433","https://openalex.org/W1612115297","https://openalex.org/W1686829286","https://openalex.org/W1811300421","https://openalex.org/W1869556422","https://openalex.org/W1902070538","https://openalex.org/W1964070472","https://openalex.org/W1964136783","https://openalex.org/W1964563874","https://openalex.org/W1966034912","https://openalex.org/W1966287322","https://openalex.org/W1966333302","https://openalex.org/W1970212576","https://openalex.org/W1970976271","https://openalex.org/W1971627627","https://openalex.org/W1973335304","https://openalex.org/W1973698889","https://openalex.org/W1974155983","https://openalex.org/W1974346098","https://openalex.org/W1974755392","https://openalex.org/W1977074555","https://openalex.org/W1977220975","https://openalex.org/W1977913536","https://openalex.org/W1978015460","https://openalex.org/W1980238345","https://openalex.org/W1981031390","https://openalex.org/W1981038870","https://openalex.org/W1981063654","https://openalex.org/W1981643307","https://openalex.org/W1982262060","https://openalex.org/W1982581773","https://openalex.org/W1983078963","https://openalex.org/W1983209955","https://openalex.org/W1986659878","https://openalex.org/W1987946549","https://openalex.org/W1988930205","https://openalex.org/W1989342280","https://openalex.org/W1995341919","https://openalex.org/W1997116991","https://openalex.org/W1999273581","https://openalex.org/W2001127408","https://openalex.org/W2003538272","https://openalex.org/W2004332394","https://openalex.org/W2005393823","https://openalex.org/W2005494676","https://openalex.org/W2007834643","https://openalex.org/W2009694692","https://openalex.org/W2010072984","https://openalex.org/W2010802663","https://openalex.org/W2011182998","https://openalex.org/W2011368435","https://openalex.org/W2011935650","https://openalex.org/W2012062489","https://openalex.org/W2012428879","https://openalex.org/W2012976574","https://openalex.org/W2013417994","https://openalex.org/W2013439481","https://openalex.org/W2016182223","https://openalex.org/W2020153219","https://openalex.org/W2020258288","https://openalex.org/W2023754051","https://openalex.org/W2025453278","https://openalex.org/W2031501875","https://openalex.org/W2031784732","https://openalex.org/W2032572332","https://openalex.org/W2033952713","https://openalex.org/W2035079959","https://openalex.org/W2035173308","https://openalex.org/W2035990937","https://openalex.org/W2036056640","https://openalex.org/W2036413866","https://openalex.org/W2038852268","https://openalex.org/W2040815697","https://openalex.org/W2041364558","https://openalex.org/W2042039316","https://openalex.org/W2043532664","https://openalex.org/W2044143571","https://openalex.org/W2044753695","https://openalex.org/W2046101549","https://openalex.org/W2046351805","https://openalex.org/W2046613226","https://openalex.org/W2046899724","https://openalex.org/W2050732932","https://openalex.org/W2051195827","https://openalex.org/W2052645364","https://openalex.org/W2053453415","https://openalex.org/W2055762199","https://openalex.org/W2056558678","https://openalex.org/W2057569652","https://openalex.org/W2058688199","https://openalex.org/W2058854441","https://openalex.org/W2062677855","https://openalex.org/W2065660929","https://openalex.org/W2066378723","https://openalex.org/W2067041945","https://openalex.org/W2067580655","https://openalex.org/W2070039108","https://openalex.org/W2074489147","https://openalex.org/W2075567596","https://openalex.org/W2078080115","https://openalex.org/W2079365712","https://openalex.org/W2079400692","https://openalex.org/W2079741631","https://openalex.org/W2081143019","https://openalex.org/W2081720252","https://openalex.org/W2086624844","https://openalex.org/W2088926870","https://openalex.org/W2089028133","https://openalex.org/W2089645967","https://openalex.org/W2090558596","https://openalex.org/W2091738279","https://openalex.org/W2092590148","https://openalex.org/W2093675399","https://openalex.org/W2093942099","https://openalex.org/W2098285719","https://openalex.org/W2099413771","https://openalex.org/W2101196233","https://openalex.org/W2104060931","https://openalex.org/W2106191211","https://openalex.org/W2107602305","https://openalex.org/W2108704847","https://openalex.org/W2109986682","https://openalex.org/W2112146239","https://openalex.org/W2113893001","https://openalex.org/W2117489143","https://openalex.org/W2120821303","https://openalex.org/W2123321877","https://openalex.org/W2124889948","https://openalex.org/W2126160338","https://openalex.org/W2133281397","https://openalex.org/W2135622428","https://openalex.org/W2140682373","https://openalex.org/W2144346774","https://openalex.org/W2144846366","https://openalex.org/W2148445249","https://openalex.org/W2158120696","https://openalex.org/W2160080582","https://openalex.org/W2160351409","https://openalex.org/W2162368141","https://openalex.org/W2162826883","https://openalex.org/W2165011357","https://openalex.org/W2201539126","https://openalex.org/W2250438075","https://openalex.org/W2270550182","https://openalex.org/W2309301194","https://openalex.org/W2315898665","https://openalex.org/W2316453713","https://openalex.org/W2318204735","https://openalex.org/W2321910355","https://openalex.org/W2323827564","https://openalex.org/W2330451690","https://openalex.org/W2331520711","https://openalex.org/W2332717221","https://openalex.org/W2342316458","https://openalex.org/W2373615029","https://openalex.org/W2425867335","https://openalex.org/W2481446166","https://openalex.org/W2481945907","https://openalex.org/W2483954911","https://openalex.org/W2485904635","https://openalex.org/W2488264223","https://openalex.org/W2496539805","https://openalex.org/W2498964030","https://openalex.org/W2561954461","https://openalex.org/W2752853835","https://openalex.org/W2753533763","https://openalex.org/W2801340078","https://openalex.org/W2890823142","https://openalex.org/W2898916015","https://openalex.org/W2912821936","https://openalex.org/W3028470905","https://openalex.org/W3035235874","https://openalex.org/W3108159662","https://openalex.org/W3135472375","https://openalex.org/W4210937892","https://openalex.org/W4214704381","https://openalex.org/W4232710988","https://openalex.org/W4234903568","https://openalex.org/W4234946427","https://openalex.org/W4235053838","https://openalex.org/W4235941905","https://openalex.org/W4237888283","https://openalex.org/W4244373888","https://openalex.org/W4250725077","https://openalex.org/W4252647391","https://openalex.org/W4253391420","https://openalex.org/W4254545912","https://openalex.org/W4254704602","https://openalex.org/W4255645218","https://openalex.org/W4285719527","https://openalex.org/W4289920060","https://openalex.org/W4292887282"],"related_works":["https://openalex.org/W2370236282","https://openalex.org/W3156023083","https://openalex.org/W1995047307","https://openalex.org/W3164313706","https://openalex.org/W1969557273","https://openalex.org/W2023689870","https://openalex.org/W2170271555","https://openalex.org/W2952318043","https://openalex.org/W4281713237","https://openalex.org/W2141684379"],"abstract_inverted_index":{"Just":[0],"when":[1],"modern":[2,59],"computers":[3,114],"(digital,":[4],"electronic,":[5],"and":[6,14,37,48,83,102,120],"programmable)":[7],"were":[8],"being":[9],"invented,":[10],"John":[11],"von":[12],"Neumann":[13,65,101],"Herman":[15],"Goldstine":[16,84,103],"wrote":[17],"a":[18,71],"paper":[19,60,94],"to":[20,31,38,69,76,125],"illustrate":[21],"the":[22,33,40,49,57,78,87,110],"mathematical":[23,72],"analyses":[24],"that":[25,68],"they":[26,106,121],"believed":[27],"would":[28,108],"be":[29,109],"needed":[30],"use":[32],"new":[34],"machines":[35],"effectively":[36],"guide":[39],"development":[41],"of":[42,51,89],"still":[43],"faster":[44],"computers.":[45],"Their":[46],"foresight":[47],"congruence":[50],"historical":[52],"events":[53],"made":[54],"their":[55,93],"work":[56],"first":[58,79],"in":[61],"numerical":[62],"analysis.":[63],"Von":[64,100],"once":[66,113],"remarked":[67],"found":[70],"theory":[73],"one":[74],"had":[75],"prove":[77],"theorem,":[80],"which":[81],"he":[82],"did":[85],"for":[86,117],"accuracy":[88],"mechanized":[90],"Gaussian":[91],"elimination\u2014but":[92],"was":[95],"about":[96],"more":[97],"than":[98],"that.":[99],"described":[104],"what":[105],"surmized":[107],"significant":[111],"questions":[112],"became":[115],"available":[116],"computational":[118],"science,":[119],"suggested":[122],"enduring":[123],"ways":[124],"answer":[126],"them.":[127]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
