{"id":"https://openalex.org/W1989339867","doi":"https://doi.org/10.1016/s0010-4485(97)00086-9","title":"Efficient and reliable methods for rounded-interval arithmetic","display_name":"Efficient and reliable methods for rounded-interval arithmetic","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W1989339867","doi":"https://doi.org/10.1016/s0010-4485(97)00086-9","mag":"1989339867"},"language":"en","primary_location":{"id":"doi:10.1016/s0010-4485(97)00086-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(97)00086-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/s0010-4485(97)00086-9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010041881","display_name":"Stephen L. Abrams","orcid":"https://orcid.org/0000-0003-2326-6672"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S.L. Abrams","raw_affiliation_strings":["Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003429353","display_name":"W. Cho","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Cho","raw_affiliation_strings":["Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089205647","display_name":"Chengyang Hu","orcid":"https://orcid.org/0000-0003-2579-7282"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C.-Y. Hu","raw_affiliation_strings":["SolidWorks Corp., Concord, MA 01742. USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SolidWorks Corp., Concord, MA 01742. USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019734465","display_name":"Takashi Maekawa","orcid":"https://orcid.org/0000-0003-3896-8431"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Maekawa","raw_affiliation_strings":["Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112381010","display_name":"Nicholas M. Patrikalakis","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"N.M. Patrikalakis","raw_affiliation_strings":["Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory. Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Department of Ocean Engineering, Design Laboratory, Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068027746","display_name":"Evan C. Sherbrooke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E.C. Sherbrooke","raw_affiliation_strings":["New Technologies Inc., Cambridge, MA 02142, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New Technologies Inc., Cambridge, MA 02142, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029603338","display_name":"Xingchen Ye","orcid":"https://orcid.org/0000-0001-6851-2721"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"X. Ye","raw_affiliation_strings":["SolidWorks Corp., Concord, MA 01742. USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SolidWorks Corp., Concord, MA 01742. USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5112381010"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":4.0802,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.93839729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"8","first_page":"657","last_page":"665"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9921000003814697,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.9624736309051514},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.7282776832580566},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6655453443527222},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5962852835655212},{"id":"https://openalex.org/keywords/double-precision-floating-point-format","display_name":"Double-precision floating-point format","score":0.5669693946838379},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5639188289642334},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5354134440422058},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5122482180595398},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.48235172033309937},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4736006557941437},{"id":"https://openalex.org/keywords/ieee-floating-point","display_name":"IEEE floating point","score":0.43847522139549255},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.43778687715530396},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.424316942691803},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4226200580596924},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37230661511421204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1132037341594696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0882517397403717}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9624736309051514},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.7282776832580566},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6655453443527222},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5962852835655212},{"id":"https://openalex.org/C35912277","wikidata":"https://www.wikidata.org/wiki/Q1243369","display_name":"Double-precision floating-point format","level":3,"score":0.5669693946838379},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5639188289642334},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5354134440422058},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5122482180595398},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.48235172033309937},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4736006557941437},{"id":"https://openalex.org/C137231763","wikidata":"https://www.wikidata.org/wiki/Q828287","display_name":"IEEE floating point","level":3,"score":0.43847522139549255},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.43778687715530396},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.424316942691803},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4226200580596924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37230661511421204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1132037341594696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0882517397403717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0010-4485(97)00086-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(97)00086-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0010-4485(97)00086-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(97)00086-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1505577863","https://openalex.org/W1538266553","https://openalex.org/W1831896804","https://openalex.org/W1972976946","https://openalex.org/W2018364992","https://openalex.org/W2044454977","https://openalex.org/W2065331993","https://openalex.org/W2066211930","https://openalex.org/W2066253548","https://openalex.org/W2077080517","https://openalex.org/W2169004268","https://openalex.org/W2611598995","https://openalex.org/W2913883396","https://openalex.org/W4233790968","https://openalex.org/W4243672067","https://openalex.org/W6630269339","https://openalex.org/W6632323159","https://openalex.org/W6758846396"],"related_works":["https://openalex.org/W2159910647","https://openalex.org/W2116803521","https://openalex.org/W2551094850","https://openalex.org/W3039927303","https://openalex.org/W4241745618","https://openalex.org/W1633207239","https://openalex.org/W2145504461","https://openalex.org/W2937715180","https://openalex.org/W2041998527","https://openalex.org/W2802515667"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"efficient":[3],"and":[4,82,87,90,93],"reliable":[5],"method":[6],"for":[7,24,40,71],"computing":[8],"the":[9,20,51,72],"unit-in-the-last-place":[10],"(ulp)":[11],"of":[12,19,50,74,76,80,85],"a":[13],"double-precision":[14],"floating-point":[15],"number,":[16],"taking":[17],"advantage":[18],"standard":[21,52],"binary":[22],"representation":[23],"floatingpoint":[25],"numbers":[26],"defined":[27,55],"by":[28,56],"IEEE":[29],"Std":[30],"754-1985.":[31],"The":[32],"ulp":[33],"is":[34],"necessary":[35],"to":[36,66],"perform":[37],"software":[38,69],"rounding":[39,53],"robust":[41,68],"rounded-interval":[42],"arithmetic":[43],"(RIA)":[44],"operations.":[45],"Hardware":[46],"rounding,":[47],"using":[48],"two":[49],"modes":[54],"IEEE-754,":[57],"may":[58],"be":[59],"more":[60],"efficient.":[61],"RIA":[62],"has":[63],"been":[64],"used":[65],"produce":[67],"systems":[70,75],"solution":[73],"nonlinear":[77],"equations,":[78],"interrogation":[79],"geometric":[81],"differential":[83],"properties":[84],"curves":[86],"surfaces,":[88],"curve":[89],"surface":[91],"intersections,":[92],"solid":[94],"modeling.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-04T09:04:59.091469","created_date":"2025-10-10T00:00:00"}
