{"id":"https://openalex.org/W2145476327","doi":"https://doi.org/10.1145/1277500.1277505","title":"Computing numerically with functions instead of numbers","display_name":"Computing numerically with functions instead of numbers","publication_year":2007,"publication_date":"2007-07-25","ids":{"openalex":"https://openalex.org/W2145476327","doi":"https://doi.org/10.1145/1277500.1277505","mag":"2145476327"},"language":"en","primary_location":{"id":"doi:10.1145/1277500.1277505","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277505","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international workshop on Symbolic-numeric computation","raw_type":"proceedings-article"},"type":"conference-abstract","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/A5065363123","display_name":"Lloyd N. Trefethen","orcid":"https://orcid.org/0000-0003-2504-1709"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lloyd N. Trefethen","raw_affiliation_strings":["Oxford University, Oxford, UK","Oxford University, Oxford, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford University, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Oxford University, Oxford, UK#TAB#","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065363123"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"28","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.996399998664856,"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":0.996399998664856,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9901999831199646,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9588000178337097,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pruning","display_name":"Pruning","score":0.6446407437324524},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6421325206756592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5472230911254883},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5467889308929443},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5084608793258667},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.49145281314849854},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4783210754394531},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4633524715900421},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44471079111099243},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.44410961866378784},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42503225803375244},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42185139656066895},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4133037030696869},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38101667165756226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08711206912994385}],"concepts":[{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.6446407437324524},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6421325206756592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5472230911254883},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5467889308929443},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5084608793258667},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.49145281314849854},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4783210754394531},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4633524715900421},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44471079111099243},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.44410961866378784},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42503225803375244},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42185139656066895},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4133037030696869},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38101667165756226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08711206912994385},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277500.1277505","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277505","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international workshop on Symbolic-numeric computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.7599999904632568,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W125503916","https://openalex.org/W1511726671","https://openalex.org/W1533404702","https://openalex.org/W1966287322","https://openalex.org/W1971545142","https://openalex.org/W1981115560","https://openalex.org/W2006141568","https://openalex.org/W2013737143","https://openalex.org/W2056522847","https://openalex.org/W2059998776","https://openalex.org/W2063208261","https://openalex.org/W2064727561","https://openalex.org/W2130694104","https://openalex.org/W2142567026","https://openalex.org/W3022136271","https://openalex.org/W3022909171"],"related_works":["https://openalex.org/W2373300491","https://openalex.org/W2395294869","https://openalex.org/W2378744544","https://openalex.org/W2594301978","https://openalex.org/W2379704676","https://openalex.org/W1998810860","https://openalex.org/W4298290365","https://openalex.org/W2797276658","https://openalex.org/W2580524192","https://openalex.org/W154587196"],"abstract_inverted_index":{"If":[0],"we":[1],"make":[2],"a":[3],"sequence":[4],"of":[5,38,63,93],"computations":[6],"involving":[7],"rational":[8],"numbers,":[9],"the":[10,41,88,100],"numerators":[11],"and":[12,40,75,81,110],"denominators":[13],"tend":[14],"to":[15,27,59,90,98],"grow":[16],"exponentially":[17],"in":[18],"length;":[19],"floating-point":[20],"arithmetic":[21],"contains":[22],"this":[23,84],"growth":[24],"by":[25,56],"pruning":[26,87],"16":[28],"digits":[29,62,92],"at":[30,95],"each":[31,96],"step.":[32],"We":[33],"present":[34],"an":[35,51],"analogous":[36],"set":[37],"ideas,":[39],"\"chebfun\"":[42],"software":[43],"system,":[44],"for":[45],"computing":[46],"with":[47,107],"piecewise-smooth":[48],"functions":[49],"on":[50],"interval.":[52],"Functions":[53],"are":[54,77],"represented":[55],"Chebyshev":[57],"series":[58],"approximately":[60],"15":[61,91],"precision.":[64],"Operations":[65],"such":[66],"as":[67],"+,":[68],"--,":[69],"x,":[70],"/,":[71],"max,":[72],"min,":[73],"norm,":[74],"zerofinding":[76],"carried":[78],"out":[79],"fast":[80],"accurately":[82],"within":[83],"context,":[85],"always":[86],"accuracy":[89],"precision":[94],"step":[97],"contain":[99],"combinatorial":[101],"explosion.":[102],"This":[103],"is":[104],"joint":[105],"work":[106],"Zachary":[108],"Battles":[109],"Ricardo":[111],"Pach\u00f3n.":[112]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
