{"id":"https://openalex.org/W7160935423","doi":"https://doi.org/10.48550/arxiv.2605.09057","title":"Local Legendre Frame Approximation from Equispaced Data","display_name":"Local Legendre Frame Approximation from Equispaced Data","publication_year":2026,"publication_date":"2026-05-09","ids":{"openalex":"https://openalex.org/W7160935423","doi":"https://doi.org/10.48550/arxiv.2605.09057"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.09057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09057","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.2605.09057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052469556","display_name":"Benxue Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Benxue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135965342","display_name":"Zhenyu Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Zhenyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135987520","display_name":"Chenyang Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Chenyang","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.45820000767707825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.45820000767707825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.04969999939203262,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.04470000043511391,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7228999733924866},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.5412999987602234},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4702000021934509},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4465999901294708},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.42730000615119934},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.42399999499320984},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.41780000925064087},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4059000015258789}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7247999906539917},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7228999733924866},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5083000063896179},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4702000021934509},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4618000090122223},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.42730000615119934},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4059000015258789},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33090001344680786},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.274399995803833},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.09057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09057","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.2605.09057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09057","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":{"We":[0,81],"propose":[1],"a":[2,15,49,58,77,83,153],"local":[3,55,71,157],"Legendre":[4],"frame":[5],"(LLF)":[6],"method":[7,39,75,135],"for":[8,86,103,160],"function":[9],"approximation":[10,26,158],"from":[11],"equispaced":[12,28,161],"data":[13],"on":[14,143],"finite":[16],"interval.":[17],"Motivated":[18],"by":[19,57],"the":[20,32,35,38,41,69,74,87,134],"difficulty":[21],"of":[22,34],"stable":[23,154],"high-order":[24],"polynomial":[25],"at":[27],"points,":[29],"especially":[30],"in":[31],"presence":[33],"Runge":[36],"phenomenon,":[37],"partitions":[40],"interval":[42],"into":[43],"subintervals,":[44],"maps":[45],"each":[46],"subinterval":[47],"to":[48,114],"common":[50],"reference":[51],"interval,":[52],"and":[53,90,106,155],"computes":[54],"coefficients":[56],"truncated":[59],"singular":[60],"value":[61],"decomposition":[62],"(TSVD)":[63],"regularization.":[64],"Since":[65],"all":[66],"subintervals":[67],"share":[68],"same":[70],"sampling":[72,124],"matrix,":[73],"admits":[76],"natural":[78],"offline--online":[79],"implementation.":[80],"establish":[82],"quasi-optimal":[84],"estimate":[85],"regularized":[88],"reconstruction":[89],"discuss":[91],"practical":[92],"parameter":[93],"selection.":[94],"Numerical":[95],"results":[96,148],"show":[97],"that":[98,150],"LLF":[99,151],"attains":[100],"high":[101],"accuracy":[102,120],"relatively":[104],"smooth":[105,129],"moderately":[107],"oscillatory":[108,116],"functions,":[109,117],"while":[110],"it":[111],"remains":[112],"applicable":[113],"highly":[115],"although":[118],"comparable":[119],"generally":[121],"requires":[122],"more":[123],"points.":[125],"For":[126],"continuous":[127],"piecewise":[128],"functions":[130],"with":[131],"derivative":[132],"singularities,":[133],"also":[136],"provides":[137,152],"an":[138],"effective":[139],"detect--localize--correct":[140],"strategy":[141],"based":[142],"one-sided":[144],"coefficient-energy":[145],"indicators.":[146],"These":[147],"indicate":[149],"flexible":[156],"framework":[159],"data.":[162]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-13T00:00:00"}
