{"id":"https://openalex.org/W2146607372","doi":"https://doi.org/10.1109/mcise.2002.1014982","title":"Fitting nature's basic functions. Part III: exponentials, sinusoids, and nonlinear least squares","display_name":"Fitting nature's basic functions. Part III: exponentials, sinusoids, and nonlinear least squares","publication_year":2002,"publication_date":"2002-07-01","ids":{"openalex":"https://openalex.org/W2146607372","doi":"https://doi.org/10.1109/mcise.2002.1014982","mag":"2146607372"},"language":"en","primary_location":{"id":"doi:10.1109/mcise.2002.1014982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mcise.2002.1014982","pdf_url":null,"source":{"id":"https://openalex.org/S107923245","display_name":"Computing in Science & Engineering","issn_l":"1521-9615","issn":["1521-9615","1558-366X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320061","host_organization_name":"AIP Publishing","host_organization_lineage":["https://openalex.org/P4310320061","https://openalex.org/P4310320257"],"host_organization_lineage_names":["AIP Publishing","American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing in Science &amp; Engineering","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/A5109247627","display_name":"B. W. Rust","orcid":null},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"B.W. Rust","raw_affiliation_strings":["National Institute for Standards and Technology, Gaithersburg, MD, USA","Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA"],"affiliations":[{"raw_affiliation_string":"National Institute for Standards and Technology, Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]},{"raw_affiliation_string":"Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109247627"],"corresponding_institution_ids":["https://openalex.org/I1321296531"],"apc_list":null,"apc_paid":null,"fwci":1.3459,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.80077633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":"4","first_page":"72","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10017","display_name":"Geology and Paleoclimatology Research","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10017","display_name":"Geology and Paleoclimatology Research","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9592000246047974,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.7146649956703186},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6141553521156311},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6062396168708801},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5961300730705261},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5070445537567139},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.45396268367767334},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.45141178369522095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4473629295825958},{"id":"https://openalex.org/keywords/exponential-polynomial","display_name":"Exponential polynomial","score":0.44160598516464233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4326529800891876},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4194740056991577},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4168476462364197},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25038474798202515},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1492360532283783},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11827248334884644},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11168473958969116}],"concepts":[{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7146649956703186},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6141553521156311},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6062396168708801},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5961300730705261},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5070445537567139},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.45396268367767334},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.45141178369522095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4473629295825958},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.44160598516464233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4326529800891876},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4194740056991577},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4168476462364197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25038474798202515},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1492360532283783},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11827248334884644},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11168473958969116},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/mcise.2002.1014982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mcise.2002.1014982","pdf_url":null,"source":{"id":"https://openalex.org/S107923245","display_name":"Computing in Science & Engineering","issn_l":"1521-9615","issn":["1521-9615","1558-366X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320061","host_organization_name":"AIP Publishing","host_organization_lineage":["https://openalex.org/P4310320061","https://openalex.org/P4310320257"],"host_organization_lineage_names":["AIP Publishing","American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing in Science &amp; Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1985370915","https://openalex.org/W2031441415","https://openalex.org/W2034357076","https://openalex.org/W2061419004","https://openalex.org/W2070779353","https://openalex.org/W4213251304"],"related_works":["https://openalex.org/W1512363145","https://openalex.org/W1980801980","https://openalex.org/W3104137792","https://openalex.org/W2974079053","https://openalex.org/W2490443452","https://openalex.org/W2081498224","https://openalex.org/W2028284242","https://openalex.org/W2034969324","https://openalex.org/W2083129711","https://openalex.org/W2146607372"],"abstract_inverted_index":{"For":[0],"Part":[1,116],"II":[2],"see":[3],"ibid.":[4],"vol.3":[5,119],"no.6":[6],"(2001).":[7],"In":[8],"previous":[9],"parts":[10],"we":[11,123],"used":[12],"linear":[13,51],"least":[14],"squares":[15],"to":[16,22,30,74,125],"fit":[17],"polynomials":[18,89],"of":[19,40,109,115,145],"various":[20],"degree":[21],"the":[23,95,146],"annual":[24],"global":[25],"temperature":[26],"anomalies":[27],"for":[28,43],"1856":[29],"1999.":[31],"Polynomials":[32],"are":[33,39],"much":[34],"beloved":[35],"by":[36],"mathematicians":[37],"but":[38],"limited":[41],"value":[42],"modeling":[44],"measured":[45],"data.":[46,147],"Natural":[47],"processes":[48],"often":[49],"display":[50],"trends,":[52],"and":[53,98],"occasionally":[54],"a":[55,127,131],"constant":[56],"acceleration":[57],"process":[58],"exhibits":[59],"quadratic":[60],"variation.":[61],"However,":[62],"higher-order":[63],"polynomial":[64,100,139],"behavior":[65],"is":[66,71],"rare":[67],"in":[68,112],"nature,":[69],"which":[70],"more":[72],"likely":[73],"produce":[75],"exponentials,":[76],"sinusoids,":[77],"logistics,":[78],"Gaussians,":[79],"or":[80],"other":[81],"special":[82],"functions.":[83],"Modeling":[84],"such":[85],"behaviors":[86],"with":[87,130],"high-order":[88],"usually":[90,141],"gives":[91],"spurious":[92],"wiggles":[93],"between":[94],"data":[96],"points,":[97],"low-order":[99],"fits":[101,140],"give":[102,142],"nonrandom":[103],"residuals.":[104],"We":[105],"saw":[106],"an":[107],"example":[108,135],"this":[110],"syndrome":[111],"Figure":[113],"4":[114],"1":[117],"(ibid.":[118],"no.5":[120],"(2001)),":[121],"where":[122],"attempted":[124],"model":[126],"quasicyclic":[128],"variation":[129],"fifth-degree":[132],"polynomial.":[133],"That":[134],"also":[136],"illustrated":[137],"that":[138],"unrealistic":[143],"extrapolations":[144]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
