{"id":"https://openalex.org/W1972998910","doi":"https://doi.org/10.1137/06067300x","title":"Stable and Convergent Unsymmetric Meshless Collocation Methods","display_name":"Stable and Convergent Unsymmetric Meshless Collocation Methods","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1972998910","doi":"https://doi.org/10.1137/06067300x","mag":"1972998910"},"language":"en","primary_location":{"id":"doi:10.1137/06067300x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06067300x","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/A5047350288","display_name":"Leevan Ling","orcid":"https://orcid.org/0000-0003-1779-0101"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Leevan Ling","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085097073","display_name":"Robert Schaback","orcid":"https://orcid.org/0000-0001-7828-4355"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Schaback","raw_affiliation_strings":["University of G\u00f3ttingen"],"affiliations":[{"raw_affiliation_string":"University of G\u00f3ttingen","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047350288"],"corresponding_institution_ids":["https://openalex.org/I530967"],"apc_list":null,"apc_paid":null,"fwci":17.2998,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.99551599,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"46","issue":"3","first_page":"1097","last_page":"1115"},"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/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.9954000115394592,"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/T10264","display_name":"Asphalt Pavement Performance Evaluation","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7919979095458984},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7354683876037598},{"id":"https://openalex.org/keywords/regularized-meshless-method","display_name":"Regularized meshless method","score":0.7331873774528503},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6335079073905945},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5634666085243225},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5400406122207642},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5385130643844604},{"id":"https://openalex.org/keywords/meshfree-methods","display_name":"Meshfree methods","score":0.5030662417411804},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45013558864593506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4263332486152649},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.42086780071258545},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.3713732659816742},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35174521803855896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24453243613243103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22050827741622925},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1880282461643219},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.05786970257759094}],"concepts":[{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7919979095458984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7354683876037598},{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.7331873774528503},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6335079073905945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5634666085243225},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5400406122207642},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5385130643844604},{"id":"https://openalex.org/C162835735","wikidata":"https://www.wikidata.org/wiki/Q14866890","display_name":"Meshfree methods","level":3,"score":0.5030662417411804},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45013558864593506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4263332486152649},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.42086780071258545},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.3713732659816742},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35174521803855896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24453243613243103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22050827741622925},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1880282461643219},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.05786970257759094},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/06067300x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06067300x","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:CiteSeerX.psu:10.1.1.67.3386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.3386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.num.math.uni-goettingen.de/schaback/research/papers/SaCUMCM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.2910","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.2910","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.num.math.uni-goettingen.de/schaback/research/papers/SaCUMCM.ps","raw_type":"text"},{"id":"pmh:oai:repository.hkbu.edu.hk:math_ja-1013","is_oa":false,"landing_page_url":"https://repository.hkbu.edu.hk/math_ja/7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196872","display_name":"HKBU Institutional Repository (Hong Kong Baptist University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141568987","host_organization_name":"Hong Kong Baptist University","host_organization_lineage":["https://openalex.org/I141568987"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematics Journal Articles","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W144669444","https://openalex.org/W1486164486","https://openalex.org/W1491507172","https://openalex.org/W1521778258","https://openalex.org/W1974937117","https://openalex.org/W1978872954","https://openalex.org/W1999025826","https://openalex.org/W2014377581","https://openalex.org/W2014871337","https://openalex.org/W2030028087","https://openalex.org/W2047877145","https://openalex.org/W2051169944","https://openalex.org/W2055528045","https://openalex.org/W2075181434","https://openalex.org/W2088822475","https://openalex.org/W3188683300"],"related_works":["https://openalex.org/W2984212906","https://openalex.org/W3021318023","https://openalex.org/W2089665536","https://openalex.org/W2094296621","https://openalex.org/W2034741988","https://openalex.org/W2045174452","https://openalex.org/W2012062214","https://openalex.org/W2058788502","https://openalex.org/W2186604662","https://openalex.org/W1973842803"],"abstract_inverted_index":{"In":[0],"the":[1,33,65,68],"theoretical":[2],"part":[3],"of":[4,18,21,32,56,67],"this":[5],"paper,":[6],"we":[7],"introduce":[8],"a":[9,19,29,36,49],"simplified":[10],"proof":[11],"technique":[12,40],"for":[13],"error":[14],"bounds":[15],"and":[16,58,71],"convergence":[17],"variation":[20],"Kansa's":[22],"well-known":[23],"unsymmetric":[24],"meshless":[25,54],"collocation":[26],"method.":[27],"For":[28],"numerical":[30,72],"implementation":[31],"convergent":[34],"variation,":[35],"previously":[37],"proposed":[38],"greedy":[39],"is":[41],"coupled":[42],"with":[43],"linear":[44],"optimization.":[45],"This":[46],"algorithm":[47],"allows":[48],"fully":[50],"adaptive":[51],"on-the-fly":[52],"data-dependent":[53],"selection":[55],"test":[57],"trial":[59],"spaces.":[60],"The":[61],"new":[62],"method":[63],"satisfies":[64],"assumptions":[66],"background":[69],"theory,":[70],"experiments":[73],"demonstrate":[74],"its":[75],"stability.":[76]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}