{"id":"https://openalex.org/W1963572125","doi":"https://doi.org/10.1137/s0036142901384472","title":"Stable Approximation and Interpolation with <i>C</i><sup>1</sup> Quartic Bivariate Splines","display_name":"Stable Approximation and Interpolation with <i>C</i><sup>1</sup> Quartic Bivariate Splines","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1963572125","doi":"https://doi.org/10.1137/s0036142901384472","mag":"1963572125"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901384472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384472","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/A5064667546","display_name":"Oleg Davydov","orcid":"https://orcid.org/0000-0001-8813-9485"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Oleg Davydov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044984323","display_name":"Larry L. Schumaker","orcid":"https://orcid.org/0000-0002-8537-548X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larry L. Schumaker","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064667546"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.09119888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"39","issue":"5","first_page":"1732","last_page":"1748"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/quartic-function","display_name":"Quartic function","score":0.7576471567153931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7571251392364502},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7223284840583801},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.6538602709770203},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5515748858451843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4617905914783478},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4554429352283478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41703057289123535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31779852509498596},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.287129282951355},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10710054636001587},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08817937970161438},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.06509125232696533}],"concepts":[{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.7576471567153931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7571251392364502},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7223284840583801},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6538602709770203},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5515748858451843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4617905914783478},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4554429352283478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41703057289123535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31779852509498596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.287129282951355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10710054636001587},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08817937970161438},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.06509125232696533},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142901384472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384472","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W114470866","https://openalex.org/W1488258091","https://openalex.org/W1968956494","https://openalex.org/W1993878235","https://openalex.org/W2004437639","https://openalex.org/W2012790650","https://openalex.org/W2013882669","https://openalex.org/W2020036445","https://openalex.org/W2021868517","https://openalex.org/W2029355303","https://openalex.org/W2029768090","https://openalex.org/W2058327300","https://openalex.org/W2062618977","https://openalex.org/W2074135659"],"related_works":["https://openalex.org/W1993924584","https://openalex.org/W2136807686","https://openalex.org/W1988803644","https://openalex.org/W2006087092","https://openalex.org/W577228042","https://openalex.org/W2581017297","https://openalex.org/W2502229995","https://openalex.org/W2066758297","https://openalex.org/W2005307408","https://openalex.org/W2063237133","https://openalex.org/W2475306757","https://openalex.org/W2011036722","https://openalex.org/W2064172716","https://openalex.org/W2160057727","https://openalex.org/W1993236025","https://openalex.org/W2036243511","https://openalex.org/W2011624610","https://openalex.org/W1520253380","https://openalex.org/W2050051820","https://openalex.org/W2955246399"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"two":[3],"recent":[4],"algorithms":[5],"for":[6,18],"computing":[7],"C1":[8],"quartic":[9],"interpolating":[10],"splines":[11],"can":[12],"be":[13],"stabilized":[14],"to":[15],"ensure":[16],"that,":[17],"smooth":[19],"functions,":[20],"they":[21],"provide":[22],"full":[23],"approximation":[24,27],"power":[25],"with":[26],"constants":[28],"depending":[29],"only":[30],"on":[31],"the":[32,36],"smallest":[33],"angle":[34],"in":[35],"triangulation":[37],"[C.":[38],"K.":[39,51,74],"Chui":[40,52,75],"and":[41,53,71,76],"D.":[42,54,64],"Hong,":[43,55,65],"Math.":[44],"Comp.,":[45],"65":[46],"(1996),":[47],"pp.":[48,62,85],"85--98;":[49],"C.":[50,73],"SIAM":[56],"J.":[57],"Numer.":[58],"Anal.,":[59],"34":[60],"(1997),":[61],"1472--1482;":[63],"Approximation":[66,70],"Theory":[67],"VIII,":[68],"Vol.1:":[69],"Interpolation,":[72],"L.":[77,78],"Schumaker,":[79],"eds.,":[80],"World":[81],"Scientific,":[82],"Singapore,":[83],"1995,":[84],"249--256].":[86]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}