{"id":"https://openalex.org/W2139724308","doi":"https://doi.org/10.1109/asap.2008.4580185","title":"An efficient method for evaluating polynomial and rational function approximations","display_name":"An efficient method for evaluating polynomial and rational function approximations","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W2139724308","doi":"https://doi.org/10.1109/asap.2008.4580185","mag":"2139724308"},"language":"en","primary_location":{"id":"doi:10.1109/asap.2008.4580185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asap.2008.4580185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 International Conference on Application-Specific Systems, Architectures and Processors","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-00761652","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058275399","display_name":"Nicolas Brisebarre","orcid":"https://orcid.org/0000-0002-4220-2132"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Brisebarre","raw_affiliation_strings":["LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon,","Ecole Normale Super. de Lyon, LIP - Arenaire (CNRS - ENS Lyon - INRIA - UCBL), Lyon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon,","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Ecole Normale Super. de Lyon, LIP - Arenaire (CNRS - ENS Lyon - INRIA - UCBL), Lyon","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I29607241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046162533","display_name":"Sylvain Chevillard","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sylvain Chevillard","raw_affiliation_strings":["LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46,","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004115757","display_name":"M.D. Ercegovac","orcid":"https://orcid.org/0009-0009-4359-0876"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Milos D. Ercegovac","raw_affiliation_strings":["Computer Science Department, 4732 Boelter Hall, University of California at Los Angeles, 90095, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, 4732 Boelter Hall, University of California at Los Angeles, 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046395330","display_name":"Jean\u2010Michel Muller","orcid":"https://orcid.org/0000-0003-3588-0047"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Michel Muller","raw_affiliation_strings":["LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46,","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048005923","display_name":"Serge Torres","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Serge Torres","raw_affiliation_strings":["LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP - Ar\u00e9naire (CNRS - ENS Lyon - INRIA - UCBL), \u00c9cole Normale Sup\u00e9rieure de Lyon, 46","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5711,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.62421712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"233","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":1.0,"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":1.0,"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":0.9962000250816345,"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":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.7251771092414856},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5616276264190674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5286087393760681},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.521876871585846},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5168209671974182},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4637473225593567},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45276087522506714},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3987017869949341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3740066587924957},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3661361336708069},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3303273320198059},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21703171730041504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1284554898738861}],"concepts":[{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.7251771092414856},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5616276264190674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5286087393760681},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.521876871585846},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5168209671974182},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4637473225593567},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45276087522506714},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3987017869949341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3740066587924957},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3661361336708069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3303273320198059},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21703171730041504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1284554898738861},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/asap.2008.4580185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/asap.2008.4580185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 International Conference on Application-Specific Systems, Architectures and Processors","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-00761652v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00761652","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ASAP 08, Jul 2008, Leuven, Belgium. pp.233-238, ⟨10.1109/ASAP.2008.4580185⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00761652v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00761652","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ASAP 08, Jul 2008, Leuven, Belgium. pp.233-238, ⟨10.1109/ASAP.2008.4580185⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320431","display_name":"Australian National University","ror":"https://ror.org/019wvm592"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1593239996","https://openalex.org/W1982393515","https://openalex.org/W2017736478","https://openalex.org/W2043792462","https://openalex.org/W2097741017","https://openalex.org/W2111416661","https://openalex.org/W2131256658","https://openalex.org/W2136670626","https://openalex.org/W2141040012","https://openalex.org/W2165473980","https://openalex.org/W2611623725","https://openalex.org/W2916844179"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2135584473","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2964223869","https://openalex.org/W4300101996","https://openalex.org/W2165950148","https://openalex.org/W2010228859","https://openalex.org/W2799377959","https://openalex.org/W2083214991"],"abstract_inverted_index":{"In":[0,111],"this":[1,112],"paper":[2],"we":[3,114],"extend":[4],"the":[5,10,66,79,105,109],"domain":[6],"of":[7,9,39,69,137],"applicability":[8],"E-method":[11,60],"[7,":[12],"8],":[13],"as":[14],"a":[15,37,132,138],"hardware-oriented":[16],"method":[17],"for":[18,65],"evaluating":[19],"elementary":[20],"functions":[21,32,73,103],"using":[22,42],"polynomial":[23],"and":[24,30,47,71,125,134],"rational":[25,31,72,102],"function":[26],"approximations.":[27],"The":[28,59],"polynomials":[29,70],"are":[33],"computed":[34],"by":[35,101,108],"solving":[36],"system":[38],"linear":[40,123],"equations":[41],"digit-serial":[43],"iterations":[44],"on":[45,122],"simple":[46],"highly":[48],"regular":[49],"hardware.":[50],"For":[51],"convergence,":[52],"these":[53],"systems":[54],"must":[55],"be":[56],"diagonally":[57],"dominant.":[58],"offers":[61],"an":[62,97,117],"efficient":[63],"way":[64],"fixed-point":[67],"evaluation":[68],"if":[74],"their":[75],"coefficients":[76],"conform":[77],"to":[78,90,94],"diagonal":[80],"dominance":[81],"condition.":[82],"Until":[83],"now,":[84],"there":[85],"was":[86],"no":[87],"systematic":[88],"approach":[89,118],"obtain":[91],"good":[92],"approximations":[93],"f":[95],"over":[96],"interval":[98],"[a,":[99],"b]":[100],"satisfying":[104],"constraints":[106],"required":[107],"E-method.":[110],"paper,":[113],"present":[115],"such":[116],"which":[119],"is":[120],"based":[121],"programming":[124],"lattice":[126],"basis":[127],"reduction.":[128],"We":[129],"also":[130],"discuss":[131],"design":[133],"performance":[135],"characteristics":[136],"corresponding":[139],"implementation.":[140]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}