{"id":"https://openalex.org/W2013213049","doi":"https://doi.org/10.1137/09076711x","title":"Moving Least Squares via Orthogonal Polynomials","display_name":"Moving Least Squares via Orthogonal Polynomials","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2013213049","doi":"https://doi.org/10.1137/09076711x","mag":"2013213049"},"language":"en","primary_location":{"id":"doi:10.1137/09076711x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09076711x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0908.0668","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033884620","display_name":"Michael Carley","orcid":"https://orcid.org/0000-0003-2965-8984"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Carley","raw_affiliation_strings":["m.j.carley@bath.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"m.j.carley@bath.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5033884620"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.38,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60944392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"3","first_page":"1310","last_page":"1322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9991999864578247,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9991999864578247,"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/T10514","display_name":"Numerical methods in engineering","score":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/mathematics","display_name":"Mathematics","score":0.6987618207931519},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6400746703147888},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.608674943447113},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6057378053665161},{"id":"https://openalex.org/keywords/moving-least-squares","display_name":"Moving least squares","score":0.5694706439971924},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5669075846672058},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5443302392959595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49133673310279846},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.42117422819137573},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3342943787574768},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.258301317691803},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2311464548110962},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16575247049331665},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13736537098884583},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.10665389895439148},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07371503114700317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6987618207931519},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6400746703147888},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.608674943447113},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6057378053665161},{"id":"https://openalex.org/C2780580100","wikidata":"https://www.wikidata.org/wiki/Q6927143","display_name":"Moving least squares","level":2,"score":0.5694706439971924},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5669075846672058},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5443302392959595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49133673310279846},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.42117422819137573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3342943787574768},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.258301317691803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2311464548110962},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16575247049331665},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13736537098884583},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.10665389895439148},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07371503114700317},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/09076711x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09076711x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0908.0668","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0908.0668","pdf_url":"https://arxiv.org/pdf/0908.0668","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:opus.bath.ac.uk:18790","is_oa":false,"landing_page_url":"http://opus.bath.ac.uk/18790/1/orthogonal.pdf","pdf_url":"http://opus.bath.ac.uk/18790/1/orthogonal.pdf","source":{"id":"https://openalex.org/S4306401631","display_name":"The University of Bath Online Publications Store (The University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Articles"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.249.861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0908.0668v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.749.1188","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.749.1188","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0908.0668.pdf","raw_type":"text"},{"id":"pmh:oai:purehost.bath.ac.uk:openaire_cris_publications/429d57d6-b9ba-45dc-b1ca-e155688666bf","is_oa":false,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/429d57d6-b9ba-45dc-b1ca-e155688666bf","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Carley, M J 2010, 'Moving least squares via orthogonal polynomials', SIAM Journal on Scientific Computing, vol. 32, no. 3, pp. 1310-1322. https://doi.org/10.1137/09076711X","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0908.0668","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0908.0668","pdf_url":"https://arxiv.org/pdf/0908.0668","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2013213049.pdf","grobid_xml":"https://content.openalex.org/works/W2013213049.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1578934722","https://openalex.org/W1969179761","https://openalex.org/W1981745143","https://openalex.org/W1991174828","https://openalex.org/W2005033578","https://openalex.org/W2012876210","https://openalex.org/W2019091792","https://openalex.org/W2052238589","https://openalex.org/W2054388475","https://openalex.org/W2056523750","https://openalex.org/W2085046308","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W4256688787","https://openalex.org/W2372558617","https://openalex.org/W2765325714","https://openalex.org/W2094510637","https://openalex.org/W2068480755","https://openalex.org/W318735075","https://openalex.org/W2743969637","https://openalex.org/W2070727579","https://openalex.org/W304801059","https://openalex.org/W1984910745"],"abstract_inverted_index":{"A":[0],"method":[1,26,38,49,95,112],"for":[2],"moving":[3,35],"least":[4,36],"squares":[5,37],"interpolation":[6],"and":[7,24,31,60,72,75,91,105,119],"differentiation":[8],"is":[9,50,113],"presented":[10],"in":[11,33,45,70,78],"the":[12,34,46,56,80,94,106],"framework":[13],"of":[14,43,58,63,82,93,108],"orthogonal":[15],"polynomials":[16],"on":[17,66,85],"discrete":[18],"points.":[19],"This":[20],"yields":[21],"a":[22],"robust":[23],"efficient":[25],"which":[27],"can":[28],"avoid":[29],"singularities":[30],"breakdowns":[32],"caused":[39],"by":[40,52,76],"particular":[41],"configurations":[42],"nodes":[44],"system.":[47],"The":[48,89,111],"tested":[51],"applying":[53],"it":[54],"to":[55,100,115],"estimation":[57],"first":[59],"second":[61,83],"derivatives":[62,84],"test":[64],"functions":[65],"random":[67],"point":[68],"distributions":[69],"two":[71],"three":[73],"dimensions":[74],"examining":[77],"detail":[79],"evaluation":[81],"one":[86],"selected":[87],"configuration.":[88],"accuracy":[90],"convergence":[92],"are":[96],"examined":[97],"with":[98],"respect":[99],"length":[101],"scale":[102],"(point":[103],"separation)":[104],"number":[107],"points":[109],"used.":[110],"found":[114],"be":[116],"robust,":[117],"accurate,":[118],"convergent.":[120]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-31T07:19:18.363097","created_date":"2020-11-23T00:00:00"}
