{"id":"https://openalex.org/W4405011997","doi":"https://doi.org/10.1137/23m1593243","title":"Stable and Accurate Least Squares Radial Basis Function Approximations on Bounded Domains","display_name":"Stable and Accurate Least Squares Radial Basis Function Approximations on Bounded Domains","publication_year":2024,"publication_date":"2024-12-04","ids":{"openalex":"https://openalex.org/W4405011997","doi":"https://doi.org/10.1137/23m1593243"},"language":"en","primary_location":{"id":"doi:10.1137/23m1593243","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1593243","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065352983","display_name":"Ben Adcock","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ben Adcock","raw_affiliation_strings":["Simon Fraser University, Vancouver, BC V6B 5K3, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Vancouver, BC V6B 5K3, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022994939","display_name":"Daan Huybrechs","orcid":"https://orcid.org/0000-0002-0536-2647"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Daan Huybrechs","raw_affiliation_strings":["Department of Computer Science, KU Leuven, 3001 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-0536-2647","affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, 3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040587059","display_name":"C\u00e9cile Piret","orcid":"https://orcid.org/0000-0002-2857-7173"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cecile Piret","raw_affiliation_strings":["Michigan Technological University, Houghton, MI 49931-1295 USA"],"raw_orcid":"https://orcid.org/0000-0002-2857-7173","affiliations":[{"raw_affiliation_string":"Michigan Technological University, Houghton, MI 49931-1295 USA","institution_ids":["https://openalex.org/I11957088"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2167,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48265396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"62","issue":"6","first_page":"2698","last_page":"2718"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8102863430976868},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6861928701400757},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.675552487373352},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5202761292457581},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4672294557094574},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43893784284591675},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4257386028766632},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3901202380657196},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.262332558631897}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8102863430976868},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6861928701400757},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.675552487373352},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5202761292457581},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4672294557094574},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43893784284591675},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4257386028766632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3901202380657196},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.262332558631897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/23m1593243","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1593243","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/788900","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/788900","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Numerical Analysis, vol. 62 (6), (2698-2718)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p2-2302","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p2/1303","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G2366831823","display_name":null,"funder_award_id":"RGPIN-2021-611675","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7718334639","display_name":null,"funder_award_id":"C15/15/055","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1971519787","https://openalex.org/W1974322848","https://openalex.org/W1988793248","https://openalex.org/W2004797340","https://openalex.org/W2020462115","https://openalex.org/W2047877145","https://openalex.org/W2053567007","https://openalex.org/W2054959729","https://openalex.org/W2055315600","https://openalex.org/W2055528045","https://openalex.org/W2066661942","https://openalex.org/W2074985547","https://openalex.org/W2076963649","https://openalex.org/W2090536661","https://openalex.org/W2134996260","https://openalex.org/W2171553643","https://openalex.org/W2268201048","https://openalex.org/W2401023124","https://openalex.org/W2481242474","https://openalex.org/W2481312347","https://openalex.org/W2496288397","https://openalex.org/W2535009480","https://openalex.org/W2625275472","https://openalex.org/W2779258471","https://openalex.org/W2965119362","https://openalex.org/W3082188580","https://openalex.org/W3089116201","https://openalex.org/W3105082494","https://openalex.org/W3118598667","https://openalex.org/W4292166688","https://openalex.org/W4304782293","https://openalex.org/W4309118586","https://openalex.org/W4361294422","https://openalex.org/W4392858425","https://openalex.org/W4396845961"],"related_works":["https://openalex.org/W2006953814","https://openalex.org/W2542637001","https://openalex.org/W1972782945","https://openalex.org/W3212981098","https://openalex.org/W4221090543","https://openalex.org/W2130622405","https://openalex.org/W2374946871","https://openalex.org/W2109887391","https://openalex.org/W1819996744","https://openalex.org/W2903071990"],"abstract_inverted_index":{"The":[0,49],"computation":[1],"of":[2,12,21,33,44,88,95,107,117,148,165,175,194],"global":[3],"radial":[4],"basis":[5],"function":[6,58],"(RBF)":[7],"approximations":[8,84,127],"requires":[9],"the":[10,19,29,37,45,71,89,93,118,146,154,163,173,178],"solution":[11,164],"a":[13,61,76,142,159],"linear":[14,78,86,143,200],"system":[15],"which,":[16],"depending":[17],"on":[18,53,60,135],"choice":[20,116],"RBF":[22,39,65],"parameters,":[23],"may":[24],"be":[25,133],"ill-conditioned.":[26],"We":[27,80,121,152],"study":[28],"stability":[30],"and":[31,69,110,170,181],"accuracy":[32,187],"approximation":[34,50],"methods":[35],"using":[36,64,141],"Gaussian":[38],"in":[40,75,100,138,186,192],"all":[41],"scaling":[42,87,144,183],"regimes":[43],"associated":[46],"shape":[47,90],"parameter.":[48],"is":[51,97],"based":[52],"discrete":[54],"least":[55,155],"squares":[56,156],"with":[57,92,145],"samples":[59],"bounded":[62,136],"domain,":[63,179],"centers":[66,176],"both":[67],"inside":[68],"outside":[70,177],"domain.":[72],"This":[73],"results":[74],"rectangular":[77],"system.":[79],"show":[81,122],"for":[82,162],"one-dimensional":[83],"that":[85,124,172],"parameter":[91],"degrees":[94,147],"freedom":[96,149],"optimal,":[98],"resulting":[99],"constant":[101],"overlap":[102],"between":[103],"neighboring":[104],"RBF's":[105],"regardless":[106],"their":[108],"number,":[109],"we":[111],"propose":[112],"an":[113],"explicit":[114],"suitable":[115],"proportionality":[119],"constant.":[120],"numerically":[123],"highly":[125],"accurate":[126],"to":[128,158,189,196],"smooth":[129],"functions":[130],"can":[131,184],"also":[132],"obtained":[134],"domains":[137],"several":[139],"dimensions,":[140],"per":[150],"dimension.":[151],"extend":[153],"approach":[157],"collocation-based":[160],"method":[161],"elliptic":[166],"boundary":[167],"value":[168],"problems":[169],"illustrate":[171],"combination":[174],"oversampling,":[180],"optimal":[182],"result":[185],"close":[188],"machine":[190],"precision":[191],"spite":[193],"having":[195],"solve":[197],"very":[198],"ill-conditioned":[199],"systems.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
