{"id":"https://openalex.org/W2138211565","doi":"https://doi.org/10.1007/s10817-015-9339-z","title":"Formal Proofs of Rounding Error Bounds","display_name":"Formal Proofs of Rounding Error Bounds","publication_year":2015,"publication_date":"2015-08-20","ids":{"openalex":"https://openalex.org/W2138211565","doi":"https://doi.org/10.1007/s10817-015-9339-z","mag":"2138211565"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-015-9339-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-015-9339-z","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01091189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046495569","display_name":"Pierre Roux","orcid":"https://orcid.org/0000-0002-3041-7742"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I193033237","display_name":"Institut Sup\u00e9rieur de l'A\u00e9ronautique et de l'Espace (ISAE-SUPAERO)","ror":"https://ror.org/04gyj6s21","country_code":"FR","type":"education","lineage":["https://openalex.org/I193033237"]},{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre Roux","raw_affiliation_strings":["ISAE, ONERA, Toulouse, France","ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)","TOCCATA - Formally Verified Programs,   Certified Tools and Numerical Computations (Universit\u00e9 Paris-Sud ; B\u00e2timent 650 ; 91405 ORSAY CEDEX - France)","ISAE-SUPAERO - Institut Sup\u00e9rieur de l'A\u00e9ronautique et de l'Espace (ISAE - 10 av. Edouard Belin - BP 54032 - 31055 TOULOUSE Cedex 4 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISAE, ONERA, Toulouse, France","institution_ids":["https://openalex.org/I193033237","https://openalex.org/I2801658355"]},{"raw_affiliation_string":"ONERA - The French Aerospace Lab [Toulouse] (F-31055 Toulouse - France)","institution_ids":["https://openalex.org/I2801658355"]},{"raw_affiliation_string":"TOCCATA - Formally Verified Programs,   Certified Tools and Numerical Computations (Universit\u00e9 Paris-Sud ; B\u00e2timent 650 ; 91405 ORSAY CEDEX - France)","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"ISAE-SUPAERO - Institut Sup\u00e9rieur de l'A\u00e9ronautique et de l'Espace (ISAE - 10 av. Edouard Belin - BP 54032 - 31055 TOULOUSE Cedex 4 - France)","institution_ids":["https://openalex.org/I193033237"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046495569"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I193033237","https://openalex.org/I2801658355"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":3.0109,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91761091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"57","issue":"2","first_page":"135","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods 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/T11697","display_name":"Numerical Methods 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/T10126","display_name":"Logic, programming, and type systems","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.983299970626831,"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/mathematical-proof","display_name":"Mathematical proof","score":0.9222824573516846},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.9151447415351868},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7968342900276184},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.6735761165618896},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6062815189361572},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5785967707633972},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5476613640785217},{"id":"https://openalex.org/keywords/formal-proof","display_name":"Formal proof","score":0.4969623386859894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4859224855899811},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.474477082490921},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36822041869163513},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3521837592124939},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3359597325325012},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3315446376800537}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.9222824573516846},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9151447415351868},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7968342900276184},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.6735761165618896},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6062815189361572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5785967707633972},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5476613640785217},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.4969623386859894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4859224855899811},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.474477082490921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36822041869163513},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3521837592124939},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3359597325325012},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3315446376800537},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10817-015-9339-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-015-9339-z","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01091189v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01091189","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://link.springer.com/article/10.1007/s10817-015-9339-z","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01091189v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01091189","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://link.springer.com/article/10.1007/s10817-015-9339-z","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W331525950","https://openalex.org/W1508641834","https://openalex.org/W1542112699","https://openalex.org/W1553511155","https://openalex.org/W1560253649","https://openalex.org/W1822676550","https://openalex.org/W1912797367","https://openalex.org/W1995574761","https://openalex.org/W2002757059","https://openalex.org/W2020804487","https://openalex.org/W2047319360","https://openalex.org/W2130920933","https://openalex.org/W2134124371","https://openalex.org/W2162201044","https://openalex.org/W2170345902","https://openalex.org/W2207050309","https://openalex.org/W3103675537"],"related_works":["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/W4231731735","https://openalex.org/W3185976014","https://openalex.org/W2134876043"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}