{"id":"https://openalex.org/W1992153626","doi":"https://doi.org/10.1137/110827156","title":"Linear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants","display_name":"Linear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1992153626","doi":"https://doi.org/10.1137/110827156","mag":"1992153626"},"language":"en","primary_location":{"id":"doi:10.1137/110827156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110827156","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5001020230","display_name":"Georges Klein","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Georges Klein","raw_affiliation_strings":["georges.klein@unifr.ch and jean-paul.berrut@unifr.ch#TAB#"],"affiliations":[{"raw_affiliation_string":"georges.klein@unifr.ch and jean-paul.berrut@unifr.ch#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058798246","display_name":"Jean\u2010Paul Berrut","orcid":null},"institutions":[{"id":"https://openalex.org/I154338468","display_name":"University of Fribourg","ror":"https://ror.org/022fs9h90","country_code":"CH","type":"education","lineage":["https://openalex.org/I154338468"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Jean-Paul Berrut","raw_affiliation_strings":["Department of Mathematics, University of Fribourg, Switzerland;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Fribourg, Switzerland;","institution_ids":["https://openalex.org/I154338468"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001020230"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7488,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.83119107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"2","first_page":"643","last_page":"656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9911999702453613,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.9628510475158691},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8621742725372314},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.7035846710205078},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5788409113883972},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49470970034599304},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.421531617641449},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.411639004945755},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.41069650650024414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3839789628982544},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12818977236747742}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.9628510475158691},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8621742725372314},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.7035846710205078},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5788409113883972},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49470970034599304},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.421531617641449},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.411639004945755},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.41069650650024414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3839789628982544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12818977236747742},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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":2,"locations":[{"id":"doi:10.1137/110827156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110827156","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:doc.rero.ch:20120904093334-EO","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400148","display_name":"reroDoc Digital Library","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1558122728","https://openalex.org/W1981115560","https://openalex.org/W1987166016","https://openalex.org/W1990847362","https://openalex.org/W2012511353","https://openalex.org/W2014989235","https://openalex.org/W2028546901","https://openalex.org/W2043460864","https://openalex.org/W2047035051","https://openalex.org/W2049897010","https://openalex.org/W2054298708","https://openalex.org/W2063612704","https://openalex.org/W2068351005","https://openalex.org/W2072540444","https://openalex.org/W2089016145","https://openalex.org/W4206339480","https://openalex.org/W4233987899","https://openalex.org/W4238937393"],"related_works":["https://openalex.org/W2528922139","https://openalex.org/W2330640442","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4386115983","https://openalex.org/W1965041963","https://openalex.org/W2766044013","https://openalex.org/W2007426143","https://openalex.org/W56705272","https://openalex.org/W2384221708"],"abstract_inverted_index":{"Derivatives":[0],"of":[1,11,13,25,28,30],"polynomial":[2],"interpolants":[3,34],"lead":[4],"in":[5],"a":[6,23,53],"natural":[7],"way":[8],"to":[9,69],"approximations":[10],"derivatives":[12,29,63,67],"the":[14,26,48],"interpolated":[15],"function,":[16],"e.g.,":[17],"through":[18],"finite":[19,38,50],"differences.":[20],"We":[21],"extend":[22],"study":[24],"approximation":[27],"linear":[31],"barycentric":[32],"rational":[33],"and":[35,56],"present":[36],"improved":[37],"difference":[39],"formulas":[40,46],"arising":[41],"from":[42],"these":[43],"interpolants.":[44],"The":[45],"contain":[47],"classical":[49],"differences":[51],"as":[52,64,66],"special":[54],"case":[55],"are":[57],"more":[58],"stable":[59],"for":[60],"calculating":[61],"one-sided":[62],"well":[65],"close":[68],"boundaries.":[70]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
