{"id":"https://openalex.org/W2975085796","doi":"https://doi.org/10.3390/computation12030053","title":"Taylor Polynomials in a High Arithmetic Precision as Universal Approximators","display_name":"Taylor Polynomials in a High Arithmetic Precision as Universal Approximators","publication_year":2024,"publication_date":"2024-03-07","ids":{"openalex":"https://openalex.org/W2975085796","doi":"https://doi.org/10.3390/computation12030053","mag":"2975085796"},"language":"en","primary_location":{"id":"doi:10.3390/computation12030053","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/computation12030053","pdf_url":"https://www.mdpi.com/2079-3197/12/3/53/pdf?version=1709782977","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/12/3/53/pdf?version=1709782977","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022019798","display_name":"Nikolaos Bakas","orcid":"https://orcid.org/0000-0002-7297-0693"},"institutions":[{"id":"https://openalex.org/I148518341","display_name":"Cyprus Institute","ror":"https://ror.org/01q8k8p90","country_code":"CY","type":"other","lineage":["https://openalex.org/I148518341"]},{"id":"https://openalex.org/I230915877","display_name":"The American College of Greece","ror":"https://ror.org/03vkake80","country_code":"GR","type":"nonprofit","lineage":["https://openalex.org/I230915877"]}],"countries":["CY","GR"],"is_corresponding":true,"raw_author_name":"Nikolaos Bakas","raw_affiliation_strings":["Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Konstantinou Kavafi Str., 2121 Nicosia, Cyprus","Department of Information Technology & AI Lab, American College of Greece, Deree. 6 Gravias Str., Aghia Paraskevi, 15342 Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-7297-0693","affiliations":[{"raw_affiliation_string":"Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Konstantinou Kavafi Str., 2121 Nicosia, Cyprus","institution_ids":["https://openalex.org/I148518341"]},{"raw_affiliation_string":"Department of Information Technology & AI Lab, American College of Greece, Deree. 6 Gravias Str., Aghia Paraskevi, 15342 Athens, Greece","institution_ids":["https://openalex.org/I230915877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022019798"],"corresponding_institution_ids":["https://openalex.org/I148518341","https://openalex.org/I230915877"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00077059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"3","first_page":"53","last_page":"53"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980000257492065,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973000288009644,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.803128719329834},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.7683941125869751},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5752855539321899},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5355498790740967},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5105987191200256},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4968719780445099},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4693124294281006},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"Radius of convergence","score":0.4576631188392639},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4470246136188507},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4467615485191345},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.44331634044647217},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44210153818130493},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44072476029396057},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4302576780319214},{"id":"https://openalex.org/keywords/richardson-extrapolation","display_name":"Richardson extrapolation","score":0.42476779222488403},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.41846877336502075},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4055823087692261},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3616388440132141},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31824323534965515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21584361791610718},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.10269248485565186},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10116952657699585}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.803128719329834},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7683941125869751},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5752855539321899},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5355498790740967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5105987191200256},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4968719780445099},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4693124294281006},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.4576631188392639},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4470246136188507},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4467615485191345},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.44331634044647217},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44210153818130493},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44072476029396057},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4302576780319214},{"id":"https://openalex.org/C102893441","wikidata":"https://www.wikidata.org/wiki/Q1063089","display_name":"Richardson extrapolation","level":3,"score":0.42476779222488403},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.41846877336502075},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4055823087692261},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3616388440132141},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31824323534965515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21584361791610718},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.10269248485565186},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10116952657699585},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation12030053","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/computation12030053","pdf_url":"https://www.mdpi.com/2079-3197/12/3/53/pdf?version=1709782977","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1350ed0c0fb2411583eb416a8fdcf1ee","is_oa":true,"landing_page_url":"https://doaj.org/article/1350ed0c0fb2411583eb416a8fdcf1ee","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 12, Iss 3, p 53 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/12/3/53/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12030053","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Computation","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation12030053","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/computation12030053","pdf_url":"https://www.mdpi.com/2079-3197/12/3/53/pdf?version=1709782977","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4520442992","display_name":null,"funder_award_id":"810660","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2975085796.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W287953187","https://openalex.org/W306903215","https://openalex.org/W821768790","https://openalex.org/W1488435683","https://openalex.org/W1534489204","https://openalex.org/W1553773604","https://openalex.org/W1966092362","https://openalex.org/W1968228366","https://openalex.org/W1969213662","https://openalex.org/W1985585033","https://openalex.org/W2019307461","https://openalex.org/W2028050352","https://openalex.org/W2030435498","https://openalex.org/W2061330057","https://openalex.org/W2063583174","https://openalex.org/W2064055621","https://openalex.org/W2064541550","https://openalex.org/W2065806409","https://openalex.org/W2089171658","https://openalex.org/W2120575449","https://openalex.org/W2137946669","https://openalex.org/W2319783832","https://openalex.org/W2336276108","https://openalex.org/W2411402341","https://openalex.org/W2946971318","https://openalex.org/W2962802089","https://openalex.org/W3044147556","https://openalex.org/W4311057588","https://openalex.org/W4380768849","https://openalex.org/W4383198321","https://openalex.org/W4384833586","https://openalex.org/W4391002536","https://openalex.org/W6610422373","https://openalex.org/W6623215464","https://openalex.org/W6672758555","https://openalex.org/W6703540782"],"related_works":["https://openalex.org/W3048095155","https://openalex.org/W2560420848","https://openalex.org/W281295283","https://openalex.org/W1459866636","https://openalex.org/W4388931352","https://openalex.org/W1996574028","https://openalex.org/W2907768163","https://openalex.org/W2025452396","https://openalex.org/W1990056466","https://openalex.org/W2170978669"],"abstract_inverted_index":{"Function":[0],"approximation":[1,25,117,164],"is":[2,59,125],"a":[3,7,27,36,50,132,140,156,170],"fundamental":[4],"process":[5],"in":[6,11,49,87,102],"variety":[8,171],"of":[9,26,45,61,69,85,143,152,159,172],"problems":[10,97,177],"computational":[12],"mechanics,":[13],"structural":[14],"engineering,":[15],"as":[16,18,110,147,149],"well":[17,148],"other":[19],"domains":[20],"that":[21],"require":[22],"the":[23,46,56,88,103,116,122,128,144,160,183],"precise":[24,92,141],"phenomenon":[28,124],"with":[29],"an":[30],"analytic":[31],"function.":[32],"This":[33],"work":[34],"demonstrates":[35],"unified":[37],"approach":[38,58],"to":[39,90,100],"these":[40],"techniques,":[41],"utilizing":[42],"partial":[43,72],"sums":[44],"Taylor":[47,81],"series":[48],"high":[51],"arithmetic":[52],"precision.":[53],"In":[54,114],"particular,":[55,115],"proposed":[57],"capable":[60],"interpolation,":[62],"extrapolation,":[63],"numerical":[64,66],"differentiation,":[65],"integration,":[67],"solution":[68],"ordinary":[70],"and":[71,75,83,106,127,175,178],"differential":[73],"equations,":[74],"system":[76,146],"identification.":[77],"The":[78,136,163],"method":[79],"employs":[80],"polynomials":[82,138],"hundreds":[84],"digits":[86,174],"computations":[89],"obtain":[91],"results.":[93],"Interestingly,":[94],"some":[95],"well-known":[96],"are":[98,119,166],"found":[99],"arise":[101],"calculation":[104,173],"accuracy":[105],"not":[107],"methodological":[108],"inefficiencies,":[109],"would":[111],"be":[112,134,180],"expected.":[113],"errors":[118,165],"precisely":[120],"predictable,":[121],"Runge":[123],"eliminated,":[126],"extrapolation":[129],"extent":[130],"may":[131],"priory":[133],"anticipated.":[135],"attained":[137],"offer":[139],"representation":[142],"unknown":[145],"its":[150],"radius":[151],"convergence,":[153],"which":[154],"provides":[155],"rigorous":[157],"estimation":[158],"prediction":[161],"ability.":[162],"comprehensively":[167],"analyzed":[168],"for":[169],"test":[176],"can":[179],"reproduced":[181],"by":[182],"provided":[184],"computer":[185],"code.":[186]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-27T08:22:11.395708","created_date":"2025-10-10T00:00:00"}