{"id":"https://openalex.org/W7165800981","doi":"https://doi.org/10.48550/arxiv.2606.24054","title":"Computing the minimal monomial basis for multivariate Birkhoff interpolation","display_name":"Computing the minimal monomial basis for multivariate Birkhoff interpolation","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165800981","doi":"https://doi.org/10.48550/arxiv.2606.24054"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24054","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24054","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.2606.24054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002291642","display_name":"\u674e\u5458\u8d6b Li Yuanhe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuanhe, Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034111999","display_name":"Jiang Xue","orcid":"https://orcid.org/0000-0001-6688-0256"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xue, Jiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139224438","display_name":"Li Zhe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhe, Li","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/T11435","display_name":"Polynomial and algebraic computation","score":0.715499997138977,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.715499997138977,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.11100000143051147,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.043699998408555984,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8582000136375427},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.6965000033378601},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6955999732017517},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.6534000039100647},{"id":"https://openalex.org/keywords/monomial-basis","display_name":"Monomial basis","score":0.646399974822998},{"id":"https://openalex.org/keywords/trigonometric-interpolation","display_name":"Trigonometric interpolation","score":0.5701000094413757},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.5285000205039978},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.4706999957561493},{"id":"https://openalex.org/keywords/monomial-ideal","display_name":"Monomial ideal","score":0.4546999931335449}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8582000136375427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.738099992275238},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.6965000033378601},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6955999732017517},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.6534000039100647},{"id":"https://openalex.org/C46132437","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Monomial basis","level":3,"score":0.646399974822998},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.5701000094413757},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5285000205039978},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.4706999957561493},{"id":"https://openalex.org/C2777789435","wikidata":"https://www.wikidata.org/wiki/Q19369206","display_name":"Monomial ideal","level":4,"score":0.4546999931335449},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.4487999975681305},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.38940000534057617},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3878999948501587},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.359499990940094},{"id":"https://openalex.org/C119768884","wikidata":"https://www.wikidata.org/wiki/Q7597108","display_name":"Stairstep interpolation","level":4,"score":0.35260000824928284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33629998564720154},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3091000020503998},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2750999927520752},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.26249998807907104},{"id":"https://openalex.org/C41054515","wikidata":"https://www.wikidata.org/wiki/Q2000912","display_name":"Standard basis","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2572999894618988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24054","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24054","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.2606.24054","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24054","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,118],"paper":[1],"studies":[2],"algorithms":[3],"for":[4,10,33,129,136],"computing":[5],"the":[6,20,30,35,39,44,56,66,69,73,78,83,89,94,116,137,146,149],"minimal":[7,84,133],"monomial":[8,40,85,134],"basis":[9,135],"multivariate":[11,139],"Birkhoff":[12,140],"interpolation":[13,36,79,98,105,141],"problems.":[14],"Our":[15],"approach":[16],"is":[17],"built":[18],"around":[19],"notion":[21],"of":[22,48,72,148],"a":[23,121,126,131],"reverse":[24],"reduced":[25],"set,":[26],"which":[27],"serves":[28],"as":[29],"key":[31],"tool":[32],"bridging":[34],"conditions":[37,80,106],"to":[38,77,115],"basis,":[41],"thereby":[42],"avoiding":[43],"construction":[45],"and":[46,100,125],"evaluation":[47],"Vandermonde":[49],"matrices":[50],"required":[51],"in":[52],"existing":[53],"algorithms.":[54],"For":[55],"single-node":[57],"case,":[58,91],"we":[59,92],"prove":[60],"that":[61],"after":[62],"Gaussian":[63],"elimination":[64],"on":[65],"incidence":[67],"matrix,":[68],"least":[70],"monomials":[71],"polynomial":[74],"set":[75],"corresponding":[76],"precisely":[81],"constitute":[82],"basis.":[86],"To":[87],"handle":[88],"multi-node":[90],"exploit":[93],"one-to-one":[95],"correspondence":[96],"between":[97],"functionals":[99],"formal":[101],"power":[102],"series,":[103],"whereby":[104],"at":[107],"arbitrary":[108],"nonzero":[109],"nodes":[110],"can":[111],"all":[112],"be":[113],"converted":[114],"origin.":[117],"provides":[119],"both":[120],"coherent":[122],"theoretical":[123],"framework":[124],"constructive":[127],"algorithm":[128],"determining":[130],"proper":[132],"general":[138],"problem.":[142],"Numerical":[143],"examples":[144],"demonstrate":[145],"effectiveness":[147],"proposed":[150],"algorithm.":[151]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-25T00:00:00"}