{"id":"https://openalex.org/W2922132391","doi":"https://doi.org/10.1145/3264448","title":"Mathematics and Speed for Interval Arithmetic","display_name":"Mathematics and Speed for Interval Arithmetic","publication_year":2019,"publication_date":"2019-03-14","ids":{"openalex":"https://openalex.org/W2922132391","doi":"https://doi.org/10.1145/3264448","mag":"2922132391"},"language":"en","primary_location":{"id":"doi:10.1145/3264448","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3264448","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5065424864","display_name":"Ulrich Kulisch","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ulrich Kulisch","raw_affiliation_strings":["KIT, Institut f\u00fcr Angewandte Mathematik, Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KIT, Institut f\u00fcr Angewandte Mathematik, Karlsruhe, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5065424864"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5784,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68473959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"45","issue":"1","first_page":"1","last_page":"22"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9391000270843506,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.77099609375},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.6687131524085999},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6316908001899719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6167185306549072},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.6030475497245789},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.5713691115379333},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.5572056174278259},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5296867489814758},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5118598341941833},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.4960497319698334},{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.4903564453125},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.4382791817188263},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4213279187679291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40008559823036194},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27285856008529663},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.262657105922699},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13757994771003723},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1346948742866516},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.09265860915184021},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.08542340993881226}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.77099609375},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.6687131524085999},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6316908001899719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6167185306549072},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.6030475497245789},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.5713691115379333},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.5572056174278259},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5296867489814758},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5118598341941833},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.4960497319698334},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.4903564453125},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.4382791817188263},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4213279187679291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40008559823036194},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27285856008529663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.262657105922699},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13757994771003723},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1346948742866516},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.09265860915184021},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.08542340993881226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3264448","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3264448","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W153133984","https://openalex.org/W186367297","https://openalex.org/W208720135","https://openalex.org/W569070979","https://openalex.org/W633957341","https://openalex.org/W1448583346","https://openalex.org/W1482337268","https://openalex.org/W1506162491","https://openalex.org/W1536011464","https://openalex.org/W1543114422","https://openalex.org/W1846057234","https://openalex.org/W1974691580","https://openalex.org/W2004216287","https://openalex.org/W2014186618","https://openalex.org/W2044610542","https://openalex.org/W2121585261","https://openalex.org/W2122057312","https://openalex.org/W2162052809","https://openalex.org/W2164218532","https://openalex.org/W2184204630","https://openalex.org/W2474947407","https://openalex.org/W2492653455","https://openalex.org/W2568063366","https://openalex.org/W3152567310","https://openalex.org/W4213042932","https://openalex.org/W4240733703","https://openalex.org/W6686068317"],"related_works":["https://openalex.org/W2181927644","https://openalex.org/W2080666584","https://openalex.org/W2158464203","https://openalex.org/W2234346873","https://openalex.org/W2756505297","https://openalex.org/W1732167683","https://openalex.org/W2621982369","https://openalex.org/W2041091076","https://openalex.org/W2068293330","https://openalex.org/W2922132391"],"abstract_inverted_index":{"After":[0],"a":[1,148,195,262,282],"short":[2],"introduction,":[3],"the":[4,63,83,86,96,108,159,191,200,220,223,229,277],"article":[5,259,278],"begins":[6],"with":[7,138,206],"an":[8,26,78,116],"axiomatic":[9,27],"definition":[10],"of":[11,16,19,31,39,62,66,71,82,85,99,102,113,125,131,161,203,222],"rounded":[12,20],"arithmetic.":[13,145,248],"The":[14,236],"concepts":[15],"rounding":[17],"and":[18,35,41,68,141,150,182,188,214,245],"arithmetic":[21,43,97,121,156,197,216,254],"operations":[22,54,59,98,122,170],"are":[23,55,105,136,147],"defined":[24,56],"in":[25,257,302],"manner":[28],"fully":[29],"independent":[30],"special":[32],"data":[33],"formats":[34],"encodings.":[36],"Basic":[37],"properties":[38],"floating-point":[40,100,178,207,213],"interval":[42,144,155,169,189,215,247,253],"can":[44,171],"directly":[45],"be":[46,172],"derived":[47],"from":[48,291],"this":[49,258,303],"abstract":[50],"mathematical":[51,286],"model.":[52],"Interval":[53],"as":[57,174,176,217,219,255],"set":[58,64],"for":[60,95,111,123,143,185,228,242,293],"elements":[61],"\u00afIR":[65],"closed":[67,80],"connected":[69],"sets":[70],"real":[72,87,244],"numbers.":[73,88],"As":[74],"such,":[75],"they":[76],"form":[77],"algebraically":[79],"subset":[81],"powerset":[84],"This":[89],"property":[90],"leads":[91],"to":[92,129,153,298],"explicit":[93],"formulas":[94],"intervals":[101,112,124,130],"\u00afIF,":[103],"which":[104],"executable":[106],"on":[107,267,285],"computer.":[109],"Arithmetic":[110],"\u00afIF":[114,126,132],"forms":[115],"exception":[117],"free":[118],"calculus,":[119],"i.e.,":[120],"always":[127],"lead":[128],"again.":[133],"Later":[134],"sections":[135],"concerned":[137],"programming":[139],"support":[140],"hardware":[142,167],"Both":[146],"must":[149],"absolutely":[151],"necessary":[152],"move":[154],"more":[157],"into":[158],"center":[160],"scientific":[162],"computing.":[163],"With":[164],"some":[165],"minor":[166],"additions,":[168],"made":[173],"fast":[175],"simple":[177],"operations.":[179],"In":[180],"vector":[181],"matrix":[183],"spaces":[184],"real,":[186],"complex,":[187],"data,":[190],"dot":[192,201,231,238],"product":[193,202,232,239],"is":[194,233,240,300],"fundamental":[196],"operation.":[198],"Computing":[199],"two":[204],"vectors":[205],"components":[208],"exactly":[209],"substantially":[210],"speeds":[211],"up":[212],"well":[218],"accuracy":[221],"computed":[224],"result.":[225],"Hardware":[226],"needed":[227],"exact":[230,237],"very":[234],"modest.":[235],"essential":[241],"long":[243,246,263],"Section":[249],"9":[250],"illustrates":[251],"that":[252],"developed":[256],"already":[260],"has":[261],"tradition.":[264],"Products":[265],"based":[266],"these":[268],"ideas":[269],"have":[270,281],"been":[271],"available":[272],"since":[273],"1980.":[274],"Implementing":[275],"what":[276,299],"advocates":[279],"would":[280],"profound":[283],"effect":[284],"software.":[287],"Modern":[288],"processor":[289],"architecture":[290],"Intel,":[292],"example,":[294],"comes":[295],"quite":[296],"close":[297],"requested":[301],"article.":[304]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}