{"id":"https://openalex.org/W421650457","doi":"https://doi.org/10.1007/bf02253185","title":"Strict optimal a posteriori error and residual bounds for Gaussian elimination in floating-point arithmetic","display_name":"Strict optimal a posteriori error and residual bounds for Gaussian elimination in floating-point arithmetic","publication_year":1986,"publication_date":"1986-06-01","ids":{"openalex":"https://openalex.org/W421650457","doi":"https://doi.org/10.1007/bf02253185","mag":"421650457"},"language":"en","primary_location":{"id":"doi:10.1007/bf02253185","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02253185","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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/A5017551184","display_name":"Friedrich Stummel","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"F. Stummel","raw_affiliation_strings":["FB Mathematik, J. W. Goethe-Universit\u00e4t, Robert-Mayer-Strasse 10, Postfach 11 19 32, D-6000, Frankfurt am Main, Federal Republic of Germany","FB Mathematik, J. W. Goethe-Universit\u00e4t, Frankfurt am Main, Federal Republic of Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik, J. W. Goethe-Universit\u00e4t, Robert-Mayer-Strasse 10, Postfach 11 19 32, D-6000, Frankfurt am Main, Federal Republic of Germany","institution_ids":["https://openalex.org/I114090438"]},{"raw_affiliation_string":"FB Mathematik, J. W. Goethe-Universit\u00e4t, Frankfurt am Main, Federal Republic of Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017551184"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.4896,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57121495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"2","first_page":"103","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973000288009644,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973000288009644,"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/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9490000009536743,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T13487","display_name":"Statistical and numerical algorithms","score":0.9472000002861023,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.8358969688415527},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.8083736300468445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.793222188949585},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7360049486160278},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6824831962585449},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.6023476123809814},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5976707339286804},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5258318185806274},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5085524320602417},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.48952516913414},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4639977812767029},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4570903182029724},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.45265477895736694},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4006747007369995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33038872480392456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16957256197929382},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12725764513015747}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.8358969688415527},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.8083736300468445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.793222188949585},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7360049486160278},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6824831962585449},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.6023476123809814},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5976707339286804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5258318185806274},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5085524320602417},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.48952516913414},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4639977812767029},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4570903182029724},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.45265477895736694},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4006747007369995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33038872480392456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16957256197929382},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12725764513015747},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02253185","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02253185","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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":5,"referenced_works":["https://openalex.org/W1966287322","https://openalex.org/W2004798810","https://openalex.org/W2017859179","https://openalex.org/W2331226313","https://openalex.org/W3001742371"],"related_works":["https://openalex.org/W2355522169","https://openalex.org/W3039927303","https://openalex.org/W2383134623","https://openalex.org/W1989068301","https://openalex.org/W4388911419","https://openalex.org/W2061091230","https://openalex.org/W4240706710","https://openalex.org/W4242955624","https://openalex.org/W196954033","https://openalex.org/W4231731735"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
