{"id":"https://openalex.org/W7165004346","doi":"https://doi.org/10.48550/arxiv.2606.18018","title":"Anti-Gauss Lagrange interpolation: Christoffel-Darboux form, barycentric representation, and orthogonal expansion","display_name":"Anti-Gauss Lagrange interpolation: Christoffel-Darboux form, barycentric representation, and orthogonal expansion","publication_year":2026,"publication_date":"2026-06-16","ids":{"openalex":"https://openalex.org/W7165004346","doi":"https://doi.org/10.48550/arxiv.2606.18018"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.18018","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18018","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.18018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138787261","display_name":"Patricia D\u00edaz de Alba","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de Alba, Patricia D\u00edaz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070818589","display_name":"Luisa Fermo","orcid":"https://orcid.org/0000-0002-4398-8990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fermo, Luisa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100018989","display_name":"Valerio Loi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Loi, Valerio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.8007000088691711,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.8007000088691711,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.03579999879002571,"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/T10514","display_name":"Numerical methods in engineering","score":0.025800000876188278,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.8245000243186951},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.7239999771118164},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6816999912261963},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.5888000130653381},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.48649999499320984},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.47450000047683716},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.45500001311302185}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.8245000243186951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7907999753952026},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.7239999771118164},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6816999912261963},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.5888000130653381},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5292999744415283},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.48649999499320984},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4406999945640564},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.34369999170303345},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3310999870300293},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.3230000138282776},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29840001463890076},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.18018","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18018","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.18018","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18018","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,34],"paper":[1],"deals":[2],"with":[3,63],"new":[4],"formulations":[5],"of":[6,15,27,42,57,61,77],"a":[7,55],"Lagrange":[8,45],"interpolant":[9,53],"polynomial":[10],"based":[11],"on":[12],"the":[13,16,28,39,43,48,52,66,75,78],"nodes":[14],"well-known":[17],"anti-Gauss":[18,68],"rule.":[19],"A":[20,71],"first":[21],"representation":[22],"is":[23],"given":[24],"in":[25],"terms":[26],"classical":[29,44],"Christoffel-Darboux":[30],"kernel":[31],"appropriately":[32],"modified.":[33],"second":[35],"one":[36],"closely":[37],"follows":[38],"barycentric":[40],"form":[41],"polynomial,":[46],"while":[47],"third":[49],"formulation":[50],"represents":[51],"as":[54],"combination":[56],"an":[58],"orthonormal":[59],"family":[60],"polynomials":[62],"respect":[64],"to":[65],"discrete":[67],"inner":[69],"product.":[70],"numerical":[72],"test":[73],"shows":[74],"performance":[76],"explored":[79],"forms.":[80]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-18T00:00:00"}
