{"id":"https://openalex.org/W2912968240","doi":"https://doi.org/10.1145/3326229.3326247","title":"Symmetry Preserving Interpolation","display_name":"Symmetry Preserving Interpolation","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2912968240","doi":"https://doi.org/10.1145/3326229.3326247","mag":"2912968240"},"language":"en","primary_location":{"id":"doi:10.1145/3326229.3326247","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01994016/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090331108","display_name":"Erick Rodriguez Bazan","orcid":null},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210106545","display_name":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]},{"id":"https://openalex.org/I4210146074","display_name":"Analyse, G\u00e9om\u00e9trie et Mod\u00e9lisation","ror":"https://ror.org/03qgt2624","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210142324","https://openalex.org/I4210146074"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Erick Rodriguez Bazan","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d'Azur & Inria M\u00e9diterran\u00e9e, Valbonne, France","AlgebRe, geOmetrie, Modelisation et AlgoriTHmes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur & Inria M\u00e9diterran\u00e9e, Valbonne, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I201841394"]},{"raw_affiliation_string":"AlgebRe, geOmetrie, Modelisation et AlgoriTHmes","institution_ids":["https://openalex.org/I4210146074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053378534","display_name":"\u00c9velyne Hubert","orcid":"https://orcid.org/0000-0003-1456-9524"},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210106545","display_name":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]},{"id":"https://openalex.org/I4210146074","display_name":"Analyse, G\u00e9om\u00e9trie et Mod\u00e9lisation","ror":"https://ror.org/03qgt2624","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210142324","https://openalex.org/I4210146074"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Evelyne Hubert","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d'Azur & Inria M\u00e9diterran\u00e9e, Valbonne, France","AlgebRe, geOmetrie, Modelisation et AlgoriTHmes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur & Inria M\u00e9diterran\u00e9e, Valbonne, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I201841394"]},{"raw_affiliation_string":"AlgebRe, geOmetrie, Modelisation et AlgoriTHmes","institution_ids":["https://openalex.org/I4210146074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3853,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61039373,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"34","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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":0.9868999719619751,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.716421902179718},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.5550306439399719},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.5375241041183472},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.5234805345535278},{"id":"https://openalex.org/keywords/trilinear-interpolation","display_name":"Trilinear interpolation","score":0.4892832934856415},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48714038729667664},{"id":"https://openalex.org/keywords/stairstep-interpolation","display_name":"Stairstep interpolation","score":0.48594534397125244},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.450775146484375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4499073624610901},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.4317961633205414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.431369423866272},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.422349214553833},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40613698959350586},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33511537313461304},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2487727701663971},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22740399837493896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18008020520210266},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.08228716254234314}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.716421902179718},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.5550306439399719},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.5375241041183472},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5234805345535278},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.4892832934856415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48714038729667664},{"id":"https://openalex.org/C119768884","wikidata":"https://www.wikidata.org/wiki/Q7597108","display_name":"Stairstep interpolation","level":4,"score":0.48594534397125244},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.450775146484375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4499073624610901},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.4317961633205414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.431369423866272},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.422349214553833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40613698959350586},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33511537313461304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2487727701663971},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22740399837493896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18008020520210266},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.08228716254234314},{"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3326229.3326247","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01994016v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01994016","pdf_url":"https://hal.science/hal-01994016/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326247⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01994016v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01994016","pdf_url":"https://hal.science/hal-01994016/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326247⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2912968240.pdf","grobid_xml":"https://content.openalex.org/works/W2912968240.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W593785437","https://openalex.org/W1481457519","https://openalex.org/W1570469679","https://openalex.org/W1596185498","https://openalex.org/W1965778005","https://openalex.org/W2016476566","https://openalex.org/W2038527926","https://openalex.org/W2055993677","https://openalex.org/W2064486311","https://openalex.org/W2069931243","https://openalex.org/W2075184731","https://openalex.org/W2075498078","https://openalex.org/W2077870553","https://openalex.org/W2119014037","https://openalex.org/W2143920029","https://openalex.org/W2157325488","https://openalex.org/W2264065105","https://openalex.org/W2407416010","https://openalex.org/W2514984710","https://openalex.org/W2732096052","https://openalex.org/W2809228707","https://openalex.org/W3100496417","https://openalex.org/W4297936497"],"related_works":["https://openalex.org/W2036543038","https://openalex.org/W2071815454","https://openalex.org/W1983442754","https://openalex.org/W2265893536","https://openalex.org/W2355145174","https://openalex.org/W2392096499","https://openalex.org/W1956240806","https://openalex.org/W2012595140","https://openalex.org/W2162238560","https://openalex.org/W2368236742"],"abstract_inverted_index":{"The":[0,40],"article":[1,41],"addresses":[2],"multivariate":[3,49],"interpolation":[4,50,65,81,100,108,117],"in":[5,15,48,83,89],"the":[6,34,38,56,86,90,95,103],"presence":[7],"of":[8,37,79,106,115],"symmetry.":[9],"Interpolation":[10],"is":[11,20],"a":[12,21,30],"prime":[13],"tool":[14],"algebraic":[16],"computation":[17],"while":[18,51],"symmetry":[19,47,67,98],"qualitative":[22],"feature":[23],"that":[24,94],"can":[25],"be":[26],"more":[27],"relevant":[28],"to":[29,44,54,76],"mathematical":[31],"model":[32],"than":[33,71],"numerical":[35],"accuracy":[36],"parameters.":[39],"shows":[42],"how":[43],"exactly":[45],"preserve":[46,112],"exploiting":[52],"it":[53],"alleviate":[55,102],"computational":[57,104],"cost.":[58],"We":[59,92],"revisit":[60],"minimal":[61],"degree":[62],"and":[63,110],"least":[64],"with":[66],"adapted":[68,99],"bases,":[69],"rather":[70],"monomial":[72],"bases.":[73],"This":[74],"allows":[75],"construct":[77],"bases":[78,101],"invariant":[80],"spaces":[82],"blocks,":[84],"capturing":[85],"inherent":[87],"redundancy":[88],"computations.":[91],"show":[93],"so":[96],"constructed":[97],"cost":[105],"any":[107,113],"problem":[109,118],"automatically":[111],"equivariance":[114],"this":[116],"might":[119],"have.":[120]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}