{"id":"https://openalex.org/W2094567672","doi":"https://doi.org/10.1137/s0036142901383478","title":"On a Hermite Interpolation by Polynomials of Two Variables","display_name":"On a Hermite Interpolation by Polynomials of Two Variables","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2094567672","doi":"https://doi.org/10.1137/s0036142901383478","mag":"2094567672"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901383478","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901383478","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/A5088324220","display_name":"Borislav Bojanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Borislav Bojanov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101667089","display_name":"Yuan Xu","orcid":"https://orcid.org/0000-0001-9228-3818"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088324220"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.25,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.91645503,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"39","issue":"5","first_page":"1780","last_page":"1793"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9957000017166138,"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":0.9957000017166138,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9945999979972839,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8851708173751831},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.8472785949707031},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.8227120637893677},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7669190168380737},{"id":"https://openalex.org/keywords/trigonometric-interpolation","display_name":"Trigonometric interpolation","score":0.7352516055107117},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.7308370471000671},{"id":"https://openalex.org/keywords/cubic-hermite-spline","display_name":"Cubic Hermite spline","score":0.5485051274299622},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.5464020371437073},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.5089387893676758},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.5048378109931946},{"id":"https://openalex.org/keywords/stairstep-interpolation","display_name":"Stairstep interpolation","score":0.48724785447120667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4684688448905945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4158453643321991},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4038393795490265},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3856383264064789},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.3823803961277008},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.33388999104499817},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.08007484674453735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0683959424495697},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.056882262229919434}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8851708173751831},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.8472785949707031},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.8227120637893677},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7669190168380737},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.7352516055107117},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.7308370471000671},{"id":"https://openalex.org/C84607441","wikidata":"https://www.wikidata.org/wiki/Q1537263","display_name":"Cubic Hermite spline","level":5,"score":0.5485051274299622},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.5464020371437073},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.5089387893676758},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.5048378109931946},{"id":"https://openalex.org/C119768884","wikidata":"https://www.wikidata.org/wiki/Q7597108","display_name":"Stairstep interpolation","level":4,"score":0.48724785447120667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4684688448905945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4158453643321991},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4038393795490265},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3856383264064789},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.3823803961277008},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.33388999104499817},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.08007484674453735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0683959424495697},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.056882262229919434},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142901383478","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901383478","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:10.1.1.6.6685","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.6685","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://darkwing.uoregon.edu/~yuan/paper/BoXu1.ps.gz","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":12,"referenced_works":["https://openalex.org/W306248719","https://openalex.org/W829640854","https://openalex.org/W1576298279","https://openalex.org/W1976919590","https://openalex.org/W1994465471","https://openalex.org/W2000210554","https://openalex.org/W2013811797","https://openalex.org/W2017992841","https://openalex.org/W2038773382","https://openalex.org/W2045552434","https://openalex.org/W2078197553","https://openalex.org/W4243181252"],"related_works":["https://openalex.org/W2351680051","https://openalex.org/W2094567672","https://openalex.org/W1965166561","https://openalex.org/W2586096767","https://openalex.org/W4389869332","https://openalex.org/W4313680078","https://openalex.org/W2069931243","https://openalex.org/W889744554","https://openalex.org/W2368532633","https://openalex.org/W2011545635"],"abstract_inverted_index":{"A":[0],"problem":[1],"of":[2,7,17,27,46,90,105],"Hermite":[3],"interpolation":[4,13,39,48,92],"by":[5,67],"polynomials":[6],"two":[8],"variables":[9],"is":[10,49],"studied.":[11],"The":[12,44],"matches":[14],"preassigned":[15],"data":[16],"function":[18],"values":[19],"and":[20],"consecutive":[21],"normal":[22],"derivatives":[23],"on":[24,29,56,62,76],"a":[25,41,73],"set":[26],"points":[28,53,61],"several":[30],"circles":[31,64],"centered":[32],"at":[33,102],"the":[34,47,52,57,60,77,87,91,103,106],"origin.":[35],"It":[36],"includes":[37],"Lagrange":[38],"as":[40],"special":[42],"case.":[43],"uniqueness":[45],"established":[50],"when":[51],"are":[54],"equidistant":[55],"circles,":[58],"while":[59],"different":[63],"may":[65],"differ":[66],"arbitrary":[68],"rotations.":[69],"This":[70],"leads":[71],"to":[72,96],"cubature":[74],"formula":[75,89],"unit":[78],"disc,":[79],"which":[80],"can":[81],"be":[82],"given":[83],"explicitly":[84],"without":[85],"knowing":[86],"explicit":[88],"polynomial.":[93],"An":[94],"erratum":[95],"this":[97],"article":[98],"has":[99],"been":[100],"appended":[101],"end":[104],"pdf":[107],"file.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
