{"id":"https://openalex.org/W7155081060","doi":"https://doi.org/10.48550/arxiv.2604.16975","title":"Convergence theory for Hermite approximations under adaptive coordinate transformations","display_name":"Convergence theory for Hermite approximations under adaptive coordinate transformations","publication_year":2026,"publication_date":"2026-04-18","ids":{"openalex":"https://openalex.org/W7155081060","doi":"https://doi.org/10.48550/arxiv.2604.16975"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.16975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.16975","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":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.2604.16975","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090607835","display_name":"Yahya Saleh","orcid":"https://orcid.org/0000-0002-3235-217X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Saleh, Yahya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5090607835"],"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/T11804","display_name":"Quantum many-body systems","score":0.3407000005245209,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11804","display_name":"Quantum many-body systems","score":0.3407000005245209,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.27250000834465027,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.09290000051259995,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.8019000291824341},{"id":"https://openalex.org/keywords/hermite-spline","display_name":"Hermite spline","score":0.6259999871253967},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.5557000041007996},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.5267000198364258},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46619999408721924},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.43220001459121704},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.39149999618530273},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.3887999951839447}],"concepts":[{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8019000291824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7138000130653381},{"id":"https://openalex.org/C186763157","wikidata":"https://www.wikidata.org/wiki/Q5741918","display_name":"Hermite spline","level":5,"score":0.6259999871253967},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.5557000041007996},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5476999878883362},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.5267000198364258},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3887999951839447},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3621000051498413},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.31200000643730164},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.2615000009536743},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.16975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.16975","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.16975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.16975","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":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":{"Recent":[0],"work":[1],"has":[2],"shown":[3],"that":[4,132],"parameterizing":[5],"and":[6],"optimizing":[7],"coordinate":[8,40,108],"transformations":[9],"using":[10,34],"normalizing":[11,169],"flows,":[12,170],"i.e.,":[13],"invertible":[14],"neural":[15],"networks,":[16],"can":[17,110],"significantly":[18],"accelerate":[19],"the":[20,27,53,56,63,68,78,95,98,112,123,134,137,141,150,160,175],"convergence":[21,113,147,161],"of":[22,55,65,70,82,94,97,114,136,163],"spectral":[23,146],"approximations.":[24],"We":[25,100],"present":[26,101],"first":[28],"error":[29,87],"estimates":[30,88],"for":[31,149],"approximating":[32,48,62],"functions":[33,120],"Hermite":[35,71,83,115,142,152,165],"expansions":[36,84],"composed":[37],"with":[38,140],"adaptive":[39,164],"transformations.":[41],"Our":[42,154],"analysis":[43,155],"establishes":[44],"an":[45,102],"equivalence":[46],"principle:":[47],"a":[49,106,128],"function":[50,139],"$f$":[51,66],"in":[52,67,89,92,174],"span":[54,69],"transformed":[57,90],"basis":[58],"is":[59],"equivalent":[60],"to":[61,76,85],"pullback":[64],"functions.":[72],"This":[73,144],"allows":[74],"us":[75],"leverage":[77],"classical":[79],"approximation":[80],"theory":[81],"derive":[86],"coordinates":[91],"terms":[93],"regularity":[96],"pullback.":[99],"example":[103],"demonstrating":[104],"how":[105],"nonlinear":[107],"transformation":[109],"enhance":[111],"expansions.":[116],"Focusing":[117],"on":[118,168],"smooth":[119],"decaying":[121],"along":[122],"real":[124],"axis,":[125],"we":[126],"construct":[127],"monotone":[129],"transport":[130],"map":[131],"aligns":[133],"decay":[135],"target":[138],"basis.":[143],"guarantees":[145],"rates":[148],"corresponding":[151],"expansion.":[153],"provides":[156],"theoretical":[157],"insight":[158],"into":[159],"behavior":[162],"approximations":[166],"based":[167],"as":[171],"recently":[172],"explored":[173],"computational":[176],"quantum":[177],"physics":[178],"literature.":[179]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-22T00:00:00"}
