{"id":"https://openalex.org/W2059726238","doi":"https://doi.org/10.1137/0917065","title":"Verification May be Better than Estimation","display_name":"Verification May be Better than Estimation","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2059726238","doi":"https://doi.org/10.1137/0917065","mag":"2059726238"},"language":"en","primary_location":{"id":"doi:10.1137/0917065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0917065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific 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/A5012652658","display_name":"C. Falc\u00f3 Korn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Falc\u00f3 Korn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"B. H\u00f6rmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. H\u00f6rmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113468311","display_name":"Ch. Ullrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. P. Ullrich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0336,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76741047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"1013","last_page":"1017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994999766349792,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.6981968283653259},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.5771183371543884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5524982213973999},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4923795461654663},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.48331356048583984},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4762271046638489},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.46835461258888245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45287781953811646},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.44198793172836304},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43013402819633484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08188295364379883}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6981968283653259},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.5771183371543884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5524982213973999},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4923795461654663},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.48331356048583984},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4762271046638489},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.46835461258888245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45287781953811646},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.44198793172836304},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43013402819633484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08188295364379883},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0917065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0917065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific 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":4,"referenced_works":["https://openalex.org/W1575701986","https://openalex.org/W1998373364","https://openalex.org/W2013678211","https://openalex.org/W2073943554"],"related_works":["https://openalex.org/W213957756","https://openalex.org/W2610540941","https://openalex.org/W13301693","https://openalex.org/W2032140442","https://openalex.org/W4386776588","https://openalex.org/W1986933664","https://openalex.org/W2150878246","https://openalex.org/W2095507327","https://openalex.org/W1977987727","https://openalex.org/W2108562122"],"abstract_inverted_index":{"Error":[0],"bounds":[1,25,71],"for":[2,51],"an":[3],"approximate":[4],"solution":[5],"of":[6,10,46,68],"a":[7,29],"linear":[8],"system":[9],"equations":[11],"are":[12],"usually":[13],"derived":[14],"from":[15],"backward":[16],"error":[17,24,53,60],"analysis.":[18],"It":[19],"is":[20],"known":[21],"that":[22,50],"such":[23],"do":[26],"not":[27],"guarantee":[28],"certain":[30],"accuracy":[31],"in":[32],"the":[33,36,66,69],"approximation.":[34],"On":[35],"other":[37],"hand,":[38],"verification":[39,54],"provides":[40],"componentwise":[41],"guaranteed":[42],"bounds.":[43],"A":[44],"series":[45],"examples":[47],"gives":[48],"evidence":[49],"H-matrices":[52],"may":[55],"be":[56],"better":[57],"than":[58],"traditional":[59],"estimation":[61],"with":[62],"respect":[63],"to":[64],"both":[65],"quality":[67],"delivered":[70],"and":[72],"computational":[73],"performance.":[74]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}