{"id":"https://openalex.org/W4414738596","doi":"https://doi.org/10.48550/arxiv.2509.15813","title":"Polynomial approximation from diffused data: unisolvence and stability","display_name":"Polynomial approximation from diffused data: unisolvence and stability","publication_year":2025,"publication_date":"2025-09-19","ids":{"openalex":"https://openalex.org/W4414738596","doi":"https://doi.org/10.48550/arxiv.2509.15813"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.15813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.15813","pdf_url":"https://arxiv.org/pdf/2509.15813","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.15813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067455849","display_name":"Ludovico Bruni Bruno","orcid":"https://orcid.org/0000-0002-5246-8049"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bruno, Ludovico Bruni","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026527736","display_name":"Stefano De March\u0131","orcid":"https://orcid.org/0000-0002-2832-8476"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"De Marchi, Stefano","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039011924","display_name":"Giacomo Elefante","orcid":"https://orcid.org/0000-0001-5576-6802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elefante, Giacomo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067455849"],"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.6459000110626221,"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":0.6459000110626221,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7024000287055969},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.6032000184059143},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5148000121116638},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4832000136375427},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4823000133037567},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.44449999928474426},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4296000003814697},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.41760000586509705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7490000128746033},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7024000287055969},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.6032000184059143},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48190000653266907},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4296000003814697},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41760000586509705},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.375900000333786},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.367900013923645},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.27639999985694885},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.2614000141620636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.15813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.15813","pdf_url":"https://arxiv.org/pdf/2509.15813","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2509.15813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.15813","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.15813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.15813","pdf_url":"https://arxiv.org/pdf/2509.15813","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"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":{"In":[0],"this":[1],"work,":[2],"we":[3,15,92,122],"address":[4],"the":[5,30,33,39,84,87,94,97,125],"problem":[6],"of":[7,10,54,86,96,102,110],"polynomial":[8],"interpolation":[9,90,98],"non-pointwise":[11],"data.":[12],"More":[13],"specifically,":[14],"assume":[16],"that":[17],"our":[18],"input":[19],"information":[20],"comes":[21],"from":[22,72],"measurements":[23],"obtained":[24],"on":[25],"diffuse":[26],"compact":[27],"domains.":[28],"Although":[29],"nodal":[31,73],"and":[32,56,117],"diffused":[34,89],"problems":[35],"are":[36],"related":[37],"by":[38],"mean":[40],"value":[41],"theorem,":[42],"such":[43,113],"an":[44],"approach":[45],"does":[46],"not":[47],"provide":[48],"any":[49],"concrete":[50],"insights":[51],"in":[52,64,100],"terms":[53,101],"well-posedness":[55],"stability.":[57],"We":[58],"hence":[59],"develop":[60],"a":[61,77,103],"different":[62],"framework":[63],"which":[65,76],"{\\it":[66],"unisolvence}":[67],"can":[68],"be":[69],"again":[70],"recovered":[71],"results,":[74],"for":[75],"wide":[78],"literature":[79],"is":[80],"available.":[81],"To":[82],"analyze":[83],"stability":[85],"so-obtained":[88],"procedure,":[91],"characterize":[93],"norm":[95],"operator":[99],"Lebesgue":[104],"constant-like":[105],"quantity.":[106],"After":[107],"analyzing":[108],"some":[109],"its":[111],"features,":[112],"as":[114],"invariance":[115],"properties":[116],"sensitivity":[118],"to":[119],"support":[120],"overlapping,":[121],"numerically":[123],"verify":[124],"theoretical":[126],"findings.":[127]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}