{"id":"https://openalex.org/W2781280356","doi":"https://doi.org/10.1145/3134441","title":"Remark on Algorithm 539","display_name":"Remark on Algorithm 539","publication_year":2017,"publication_date":"2017-12-18","ids":{"openalex":"https://openalex.org/W2781280356","doi":"https://doi.org/10.1145/3134441","mag":"2781280356"},"language":"en","primary_location":{"id":"doi:10.1145/3134441","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3134441","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/A5110067683","display_name":"Richard Hanson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard J. Hanson","raw_affiliation_strings":["Retired"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Retired","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049958919","display_name":"Tim Hopkins","orcid":"https://orcid.org/0000-0001-6730-7398"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tim Hopkins","raw_affiliation_strings":["University of Kent, UK"],"raw_orcid":"https://orcid.org/0000-0001-6730-7398","affiliations":[{"raw_affiliation_string":"University of Kent, UK","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.23035442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"3","first_page":"1","last_page":"23"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9929999709129333,"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/floating-point","display_name":"Floating point","score":0.7058123350143433},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6807616949081421},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6388755440711975},{"id":"https://openalex.org/keywords/uniprocessor-system","display_name":"Uniprocessor system","score":0.6262618899345398},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.6064369678497314},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.490894615650177},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46666163206100464},{"id":"https://openalex.org/keywords/double-precision-floating-point-format","display_name":"Double-precision floating-point format","score":0.4647483229637146},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.42569032311439514},{"id":"https://openalex.org/keywords/single-precision-floating-point-format","display_name":"Single-precision floating-point format","score":0.41688311100006104},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4149608910083771},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09108889102935791}],"concepts":[{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.7058123350143433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6807616949081421},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6388755440711975},{"id":"https://openalex.org/C79189994","wikidata":"https://www.wikidata.org/wiki/Q3488021","display_name":"Uniprocessor system","level":3,"score":0.6262618899345398},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.6064369678497314},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.490894615650177},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46666163206100464},{"id":"https://openalex.org/C35912277","wikidata":"https://www.wikidata.org/wiki/Q1243369","display_name":"Double-precision floating-point format","level":3,"score":0.4647483229637146},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.42569032311439514},{"id":"https://openalex.org/C133095886","wikidata":"https://www.wikidata.org/wiki/Q1307173","display_name":"Single-precision floating-point format","level":3,"score":0.41688311100006104},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4149608910083771},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09108889102935791},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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/C4822641","wikidata":"https://www.wikidata.org/wiki/Q846651","display_name":"Multiprocessing","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3134441","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3134441","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"},{"id":"pmh:oai:kar.kent.ac.uk:67205","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3134441>)","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W133977063","https://openalex.org/W613436598","https://openalex.org/W1968983898","https://openalex.org/W1988425770","https://openalex.org/W1992671263","https://openalex.org/W2005242289","https://openalex.org/W2006384005","https://openalex.org/W2057711597","https://openalex.org/W2058890578","https://openalex.org/W2069936665","https://openalex.org/W2074965064","https://openalex.org/W2084231858","https://openalex.org/W3022909171","https://openalex.org/W4229666556"],"related_works":["https://openalex.org/W3150370983","https://openalex.org/W2239119680","https://openalex.org/W1564887326","https://openalex.org/W3150959508","https://openalex.org/W2116803521","https://openalex.org/W2773283032","https://openalex.org/W1571090276","https://openalex.org/W3215589575","https://openalex.org/W1973800584","https://openalex.org/W2185760795"],"abstract_inverted_index":{"We":[0,208],"propose":[1],"a":[2,29,153,156,212],"set":[3,130],"of":[4,28,38,54,70,83,95,107,131,191,202,215,238],"new":[5,145,226],"Fortran":[6,102],"reference":[7],"implementations,":[8],"based":[9],"on":[10,175,211],"an":[11],"algorithm":[12],"proposed":[13],"by":[14],"Kahan,":[15],"for":[16,68,231],"the":[17,25,42,52,55,81,84,100,111,144,189,194,200,235,239],"Level":[18],"1":[19],"BLAS":[20],"routines":[21,40,134],"*NRM2":[22],"that":[23,61,218],"compute":[24],"Euclidean":[26],"norm":[27],"real":[30],"or":[31],"complex":[32],"input":[33,112,180],"vector.":[34],"The":[35],"principal":[36],"advantage":[37],"these":[39],"over":[41],"current":[43],"offerings":[44],"is":[45,135,159],"that,":[46],"rather":[47],"than":[48],"losing":[49],"accuracy":[50,233],"as":[51,118,120,127],"length":[53,71],"vector":[56],"increases,":[57],"they":[58,185],"generate":[59],"results":[60],"are":[62,182],"accurate":[63],"to":[64,104,138,143,222],"almost":[65],"machine":[66],"precision":[67,82],"vectors":[69,181],"N":[72,74,77],"<":[73],"max":[75,78],"where":[76],"depends":[79],"upon":[80],"floating":[85,123,166],"point":[86,124,167],"arithmetic":[87,241],"being":[88],"used.":[89],"In":[90],"addition,":[91],"we":[92,151,172],"make":[93],"use":[94,201],"intrinsic":[96],"modules,":[97],"introduced":[98],"in":[99,110],"latest":[101],"standards,":[103],"detect":[105],"occurrences":[106],"non-finite":[108],"numbers":[109],"data":[113],"and":[114,228,234],"return":[115],"suitable":[116],"values":[117],"well":[119],"setting":[121],"IEEE":[122,165,240],"status":[125,242],"flags":[126,169],"appropriate.":[128],"A":[129],"C":[132],"interface":[133],"also":[136,209],"provided":[137],"allow":[139],"simple,":[140],"portable":[141],"access":[142],"routines.":[146],"To":[147],"improve":[148],"execution":[149],"speed,":[150],"advocate":[152],"hybrid":[154],"algorithm;":[155],"simple":[157,195],"loop":[158,196],"used":[160],"first":[161],"and,":[162],"only":[163],"if":[164],"exception":[168],"signal,":[170],"do":[171,186],"fall":[173],"back":[174],"Kahan\u2019s":[176,192],"algorithm.":[177],"Since":[178],"most":[179],"\u201ceasy,\u201d":[183],"i.e.,":[184],"not":[187],"require":[188],"sophistication":[190],"algorithm,":[193],"improves":[197],"performance":[198],"while":[199],"compensated":[203],"summation":[204],"ensures":[205],"high":[206],"accuracy.":[207],"report":[210],"comprehensive":[213],"suite":[214],"test":[216,223],"problems":[217],"has":[219],"been":[220],"developed":[221],"both":[224,232],"our":[225],"implementation":[227],"existing":[229],"codes":[230],"appropriate":[236],"settings":[237],"flags.":[243]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}