{"id":"https://openalex.org/W2063857110","doi":"https://doi.org/10.1137/0205017","title":"Graph Transformations for Roundoff Analysis","display_name":"Graph Transformations for Roundoff Analysis","publication_year":1976,"publication_date":"1976-06-01","ids":{"openalex":"https://openalex.org/W2063857110","doi":"https://doi.org/10.1137/0205017","mag":"2063857110"},"language":"en","primary_location":{"id":"doi:10.1137/0205017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205017","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 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/A5071092709","display_name":"Webb Miller","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Webb Miller","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071092709"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8455,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.91030393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"2","first_page":"204","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10904","display_name":"Embedded Systems Design Techniques","score":0.9692999720573425,"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/rounding","display_name":"Rounding","score":0.9433450698852539},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.9074186682701111},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.6977543234825134},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.67247474193573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.610400378704071},{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.5774725675582886},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5543870329856873},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4950632154941559},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.48902544379234314},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.48590198159217834},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39146023988723755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3445832133293152},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34177684783935547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31505706906318665},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.12774533033370972},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12362918257713318}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.9433450698852539},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.9074186682701111},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.6977543234825134},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.67247474193573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.610400378704071},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.5774725675582886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5543870329856873},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4950632154941559},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.48902544379234314},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.48590198159217834},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39146023988723755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3445832133293152},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34177684783935547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31505706906318665},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.12774533033370972},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12362918257713318},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0205017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205017","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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":9,"referenced_works":["https://openalex.org/W135423513","https://openalex.org/W147374749","https://openalex.org/W1984176077","https://openalex.org/W2012040908","https://openalex.org/W2034998146","https://openalex.org/W2041308077","https://openalex.org/W2102140633","https://openalex.org/W2135622428","https://openalex.org/W2752908210"],"related_works":["https://openalex.org/W4240706710","https://openalex.org/W1931644165","https://openalex.org/W2383134623","https://openalex.org/W2134876043","https://openalex.org/W2078634137","https://openalex.org/W1496637154","https://openalex.org/W2400766834","https://openalex.org/W187939582","https://openalex.org/W2184853271","https://openalex.org/W2017654342"],"abstract_inverted_index":{"When":[0],"analyzing":[1],"a":[2,12,68,85],"numerical":[3],"algorithm,":[4],"it":[5,29],"is":[6,19,36],"often":[7],"possible":[8],"to":[9,21,54,66,102],"show":[10],"that":[11,33],"rounding":[13,89],"error":[14,90],"at":[15,23],"one":[16],"floating-point":[17],"operation":[18],"equivalent":[20],"errors":[22],"other":[24,75],"operations.":[25],"In":[26,80],"such":[27],"cases,":[28],"can":[30,47],"be":[31,48,64],"concluded":[32],"no":[34],"generality":[35],"lost":[37],"if":[38],"certain":[39],"operations":[40],"are":[41,78,93],"considered":[42],"error-free.":[43],"Sometimes":[44],"this":[45,72,81],"conclusion":[46],"reached":[49],"automatically":[50],"and":[51,106],"inexpensively":[52],"compared":[53],"the":[55,58,110],"cost":[56],"of":[57,87,112],"ultimate":[59],"roundoff":[60],"analysis.":[61],"It":[62],"may":[63],"advantageous":[65],"use":[67],"preprocessor":[69],"which":[70,92],"performs":[71],"reduction":[73],"before":[74],"automatic":[76],"techniques":[77],"invoked.":[79],"report":[82],"we":[83],"consider":[84],"class":[86],"elementary":[88],"reductions":[91],"most":[94],"naturally":[95],"interpreted":[96],"as":[97],"graph":[98],"transformations.":[99,114],"This":[100],"leads":[101],"questions":[103],"concerning":[104],"heuristics":[105],"optimal":[107],"strategies":[108],"for":[109],"application":[111],"these":[113]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}