{"id":"https://openalex.org/W7148638700","doi":"https://doi.org/10.48550/arxiv.2604.01146","title":"A deterministic multiple-shift lattice algorithm for function approximation in Korobov and half-period Cosine spaces","display_name":"A deterministic multiple-shift lattice algorithm for function approximation in Korobov and half-period Cosine spaces","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148638700","doi":"https://doi.org/10.48550/arxiv.2604.01146"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.01146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01146","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.2604.01146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102627191","display_name":"Jiarui Du","orcid":"https://orcid.org/0009-0008-1956-6537"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Jiarui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132877445","display_name":"Josef Dick","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dick, Josef","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/T12404","display_name":"Mathematical Approximation and Integration","score":0.953000009059906,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.953000009059906,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.009999999776482582,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/lattice","display_name":"Lattice (music)","score":0.49720001220703125},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.41819998621940613},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.39480000734329224},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.3714999854564667},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.36820000410079956},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.367900013923645},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.3612000048160553},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.33640000224113464},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3346000015735626},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.3269999921321869}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7511000037193298},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3603000044822693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33980000019073486},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3165999948978424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3124000132083893},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.26420000195503235},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C140101238","wikidata":"https://www.wikidata.org/wiki/Q1404885","display_name":"Window function","level":3,"score":0.2535000145435333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.01146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01146","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.2604.01146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01146","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":{"Approximating":[0],"multivariate":[1],"periodic":[2],"functions":[3],"in":[4,95,131,184],"weighted":[5],"Korobov":[6],"spaces":[7,108],"via":[8,109],"rank-1":[9],"lattices":[10],"is":[11],"fundamentally":[12],"limited":[13],"by":[14,143],"frequency":[15,47],"aliasing.":[16],"Existing":[17],"optimal-rate":[18],"methods":[19],"rely":[20],"on":[21],"randomized":[22],"constructions":[23],"or":[24],"large":[25],"pre-computations.":[26],"We":[27,83],"propose":[28],"a":[29,40,115,156],"fully":[30],"deterministic":[31,88,193],"multiple-shift":[32],"lattice":[33],"algorithm":[34,123,154],"without":[35],"pre-computation.":[36],"First,":[37],"we":[38,63,100,119],"develop":[39],"simplified":[41],"multiple":[42],"shift":[43],"framework":[44,103],"for":[45,161],"aliased":[46],"fibers":[48],"that":[49,69,86,121],"reduces":[50],"sampling":[51,185],"costs.":[52],"Second,":[53],"leveraging":[54],"the":[55,60,72,80,91,96,110,122,132,152,168,177],"Chinese":[56],"Remainder":[57],"Theorem":[58],"and":[59,75,127],"Weil":[61],"bound,":[62],"introduce":[64],"an":[65,138,181],"adaptive":[66],"hybrid":[67],"construction":[68],"algebraically":[70],"guarantees":[71],"full":[73],"rank":[74],"bounded":[76],"condition":[77],"number":[78],"of":[79],"reconstruction":[81],"matrix.":[82],"rigorously":[84],"prove":[85,120],"this":[87,102],"method":[89],"maintains":[90],"optimal":[92,125],"convergence":[93],"rate":[94],"worst-case":[97],"setting.":[98],"Furthermore,":[99],"extend":[101],"to":[104],"non-periodic,":[105],"half-period":[106,133],"cosine":[107,134],"tent":[111],"transformation.":[112],"By":[113],"establishing":[114],"strict":[116],"projection":[117],"equivalence,":[118],"attains":[124],"$L_2$":[126],"$L_\\infty$":[128],"approximation":[129],"orders":[130],"space,":[135],"successfully":[136],"resolving":[137],"open":[139],"theoretical":[140,178],"problem":[141],"posed":[142],"Suryanarayana":[144],"et":[145],"al.":[146],"(2016).":[147],"This":[148],"mathematically":[149],"also":[150],"validates":[151],"proposed":[153],"as":[155,167],"generic":[157],"meshless":[158],"spectral":[159],"solver":[160],"high-dimensional":[162],"boundary":[163],"value":[164],"problems,":[165],"such":[166],"Poisson":[169],"equation":[170],"with":[171],"Neumann":[172],"conditions.":[173],"Numerical":[174],"experiments":[175],"corroborate":[176],"bounds,":[179],"demonstrating":[180],"order-of-magnitude":[182],"reduction":[183],"complexity":[186],"over":[187],"probabilistic":[188],"baselines":[189],"while":[190],"ensuring":[191],"absolute":[192],"stability.":[194]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-04T00:00:00"}
