{"id":"https://openalex.org/W4415135851","doi":"https://doi.org/10.1007/s10444-026-10309-4","title":"Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles","display_name":"Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W4415135851","doi":"https://doi.org/10.1007/s10444-026-10309-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10309-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10309-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10309-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10309-4.pdf","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":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Ludovico Bruni\u00a0Bruno","raw_affiliation_strings":["Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, Padua, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5246-8049","affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081317887","display_name":"Francesco Dell\u2019Accio","orcid":"https://orcid.org/0000-0003-4879-894X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francesco Dell\u2019Accio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036671307","display_name":"Wolfgang Erb","orcid":"https://orcid.org/0000-0003-3541-5401"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Wolfgang Erb","raw_affiliation_strings":["Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, Padua, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036071891","display_name":"Federico Nudo","orcid":"https://orcid.org/0000-0003-4418-3817"},"institutions":[{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Federico Nudo","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Calabria, Rende, CS, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Calabria, Rende, CS, Italy","institution_ids":["https://openalex.org/I45204951"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5067455849"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00871685,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"3","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":0.9927999973297119,"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":0.9927999973297119,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.986299991607666,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/bivariate-analysis","display_name":"Bivariate analysis","score":0.7631000280380249},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6324999928474426},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49540001153945923},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49380001425743103},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4271000027656555}],"concepts":[{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.7631000280380249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7508999705314636},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6324999928474426},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.451200008392334},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4271000027656555},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4009000062942505},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.335999995470047},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3034000098705292},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10444-026-10309-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10309-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10309-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2506.03025","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.03025","pdf_url":"https://arxiv.org/pdf/2506.03025","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2506.03025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.03025","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10444-026-10309-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10309-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10309-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1145458839","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1653392959","display_name":null,"funder_award_id":"CUP_E53C24001950001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G4561361838","display_name":null,"funder_award_id":"CUP_E53C24001950001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G5245466801","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G582555903","display_name":null,"funder_award_id":"PRIN 2022 No. 104 of February 2, 2022 and Project 2022FHCNY3","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8178972656","display_name":null,"funder_award_id":"2025 Projects","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G8348146674","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320321966","funder_display_name":"Universit\u00e0 degli Studi di Padova"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320313985","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415135851.pdf","grobid_xml":"https://content.openalex.org/works/W4415135851.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1,91],"paper":[2],"explores":[3],"the":[4,46,95,125,128,131,142,145,161],"reconstruction":[5],"of":[6,48,63,97,100,130,144],"a":[7,13,51,74,81,98,149],"real-valued":[8],"function":[9,186],"f":[10,49,79],"defined":[11],"over":[12,50],"domain":[14],"$$\\varOmega":[15,64],"\\subset":[16,104],"\\mathbb":[17],"{R}^2$$":[18],"<mml:math":[19,56,66,107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[20,57,67,108],"<mml:mrow>":[21,25,109],"<mml:mi>\u03a9</mml:mi>":[22,68],"<mml:mo>\u2282</mml:mo>":[23,114],"<mml:msup>":[24],"<mml:mi>R</mml:mi>":[26],"</mml:mrow>":[27,30,119],"<mml:mn>2</mml:mn>":[28],"</mml:msup>":[29],"</mml:math>":[31,62,69,120],"using":[32,80,160],"bivariate":[33,75],"polynomials":[34],"that":[35,44,77,181],"satisfy":[36],"triangular":[37],"histopolation":[38,82,155],"conditions.":[39],"More":[40],"precisely,":[41],"we":[42],"assume":[43],"only":[45],"averages":[47],"given":[52],"triangulation":[53],"$$\\mathcal":[54,102],"{T}_N$$":[55,106],"<mml:msub>":[58,110,115],"<mml:mi>T</mml:mi>":[59,111,116],"<mml:mi>N</mml:mi>":[60,117],"</mml:msub>":[61,113,118],"$$":[65],"are":[70,174],"available":[71],"and":[72,127,156,167,176],"seek":[73],"polynomial":[76,146],"approximates":[78],"approach,":[83],"potentially":[84,137],"flanked":[85],"by":[86],"an":[87],"additional":[88],"regression":[89],"technique.":[90],"methodology":[92],"relies":[93],"on":[94],"selection":[96],"subset":[99],"triangles":[101,135],"{T}_M":[103],"\\mathcal":[105],"<mml:mi>M</mml:mi>":[112],"for":[121],"histopolation,":[122],"ensuring":[123],"both":[124],"solvability":[126],"well-conditioning":[129],"problem.":[132],"The":[133,171],"remaining":[134],"can":[136],"be":[138],"used":[139],"to":[140],"enhance":[141],"accuracy":[143],"approximation":[147],"through":[148,178],"simultaneous":[150],"regression.":[151],"We":[152],"will":[153],"introduce":[154],"combined":[157],"histopolation-regression":[158],"methods":[159],"Padua":[162],"points,":[163],"discrete":[164],"Leja":[165],"sequences,":[166],"approximate":[168],"Fekete":[169],"nodes.":[170],"proposed":[172],"algorithms":[173],"implemented":[175],"evaluated":[177],"numerical":[179],"experiments":[180],"demonstrate":[182],"their":[183],"effectiveness":[184],"in":[185],"approximation.":[187]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-14T00:00:00"}