{"id":"https://openalex.org/W2082519520","doi":"https://doi.org/10.1109/fskd.2010.5569316","title":"On polynomial interpolation of intervals","display_name":"On polynomial interpolation of intervals","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2082519520","doi":"https://doi.org/10.1109/fskd.2010.5569316","mag":"2082519520"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2010.5569316","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2010.5569316","pdf_url":null,"source":{"id":"https://openalex.org/S4363608217","display_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-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/A5035162486","display_name":"Yongchao Hou","orcid":"https://orcid.org/0000-0001-7978-022X"},"institutions":[{"id":"https://openalex.org/I46520130","display_name":"Chaohu University","ror":"https://ror.org/00mwds915","country_code":"CN","type":"education","lineage":["https://openalex.org/I46520130"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongchao Hou","raw_affiliation_strings":["Department of Mathematics, Chaohu University, Chaohu, China","Department of Mathematics, Chaohu University, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chaohu University, Chaohu, China","institution_ids":["https://openalex.org/I46520130"]},{"raw_affiliation_string":"Department of Mathematics, Chaohu University, China","institution_ids":["https://openalex.org/I46520130"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078220656","display_name":"Haiquan Qiu","orcid":"https://orcid.org/0000-0002-2105-7351"},"institutions":[{"id":"https://openalex.org/I184681353","display_name":"Anhui University of Science and Technology","ror":"https://ror.org/00q9atg80","country_code":"CN","type":"education","lineage":["https://openalex.org/I184681353"]},{"id":"https://openalex.org/I4210109416","display_name":"Anhui Science and Technology University","ror":"https://ror.org/01pn91c28","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210109416"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiquan Qiu","raw_affiliation_strings":["College of Science, Anhui University of Science and Technology, Fengyang, China","College of Science, Anhui Science and Technology University, Fengyang, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Anhui University of Science and Technology, Fengyang, China","institution_ids":["https://openalex.org/I4210109416","https://openalex.org/I184681353"]},{"raw_affiliation_string":"College of Science, Anhui Science and Technology University, Fengyang, China","institution_ids":["https://openalex.org/I4210109416","https://openalex.org/I184681353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035162486"],"corresponding_institution_ids":["https://openalex.org/I46520130"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26527051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2280","last_page":"2284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9896000027656555,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.7136459946632385},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6948491334915161},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.6720877289772034},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.6715254783630371},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6273726224899292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5444120764732361},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5103461146354675},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4870658218860626},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.4510554075241089},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.44898536801338196},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4113847315311432},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39735478162765503},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.29701077938079834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27550172805786133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2532154321670532},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23327913880348206},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18625226616859436},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11966526508331299},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08313164114952087},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.06891727447509766}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7136459946632385},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6948491334915161},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.6720877289772034},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.6715254783630371},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6273726224899292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5444120764732361},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5103461146354675},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4870658218860626},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4510554075241089},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.44898536801338196},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4113847315311432},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39735478162765503},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.29701077938079834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27550172805786133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2532154321670532},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23327913880348206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18625226616859436},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11966526508331299},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08313164114952087},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06891727447509766},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"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":1,"locations":[{"id":"doi:10.1109/fskd.2010.5569316","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2010.5569316","pdf_url":null,"source":{"id":"https://openalex.org/S4363608217","display_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W56003785","https://openalex.org/W1580809199","https://openalex.org/W1979801620","https://openalex.org/W2013934519","https://openalex.org/W2043584297","https://openalex.org/W2060924166","https://openalex.org/W4240596267","https://openalex.org/W7038630121"],"related_works":["https://openalex.org/W1179085681","https://openalex.org/W2374545223","https://openalex.org/W2095809698","https://openalex.org/W2371738094","https://openalex.org/W2354378723","https://openalex.org/W4200281652","https://openalex.org/W2387259408","https://openalex.org/W4367556995","https://openalex.org/W2488705107","https://openalex.org/W1525419764"],"abstract_inverted_index":{"Interpolation":[0],"methods":[1],"have":[2],"been":[3],"very":[4],"popular":[5],"in":[6,109],"many":[7],"practical":[8],"problems.":[9],"To":[10],"estimate":[11],"a":[12,17,84],"function":[13],"value":[14,46],"y":[15,32],"for":[16],"given":[18],"x,":[19],"we":[20,40,58,67,76],"need":[21],"to":[22,52,126],"measure":[23],"several":[24],"pairs":[25],"of":[26,47,62,81,87,98,119,130,136],"(x":[27],"<sub":[28,33],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29,34],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[30,35],",":[31],").":[36],"In":[37,73],"some":[38],"problems,":[39],"do":[41],"not":[42],"know":[43,59],"the":[44,48,53,60,63,69,78,88,95,117,128,131,134,137],"exact":[45],"measured":[49,64],"quantities,":[50],"due":[51],"inevitable":[54],"measurement":[55],"inaccuracy.":[56],"While,":[57],"ranges":[61],"quantities;":[65],"namely,":[66],"represent":[68],"quantities":[70],"as":[71],"intervals.":[72,82],"this":[74],"paper,":[75],"study":[77],"polynomial":[79,91,101],"interpolation":[80],"First,":[83],"general":[85],"form":[86,111],"interval":[89,99],"coefficients":[90],"is":[92,102],"given.":[93],"Then,":[94],"existence":[96],"theorem":[97],"interpolating":[100],"proved.":[103],"We":[104],"give":[105],"two":[106,122],"solution":[107],"formulas,":[108],"Lagrange":[110],"and":[112,115,133],"Newton":[113],"form,":[114],"get":[116],"relations":[118],"them.":[120],"Finally,":[121],"examples":[123],"are":[124],"provided":[125],"illustrate":[127],"rationality":[129],"method":[132],"validity":[135],"solution.":[138]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}