{"id":"https://openalex.org/W2101210801","doi":"https://doi.org/10.1145/1145768.1145792","title":"Symbolic-numeric sparse interpolation of multivariate polynomials","display_name":"Symbolic-numeric sparse interpolation of multivariate polynomials","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2101210801","doi":"https://doi.org/10.1145/1145768.1145792","mag":"2101210801"},"language":"en","primary_location":{"id":"doi:10.1145/1145768.1145792","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145792","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5057638793","display_name":"Mark Giesbrecht","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mark Giesbrecht","raw_affiliation_strings":["University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001656489","display_name":"George Labahn","orcid":"https://orcid.org/0009-0005-8977-4890"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"George Labahn","raw_affiliation_strings":["University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103083848","display_name":"Wen-shin Lee","orcid":"https://orcid.org/0000-0002-2808-3739"},"institutions":[{"id":"https://openalex.org/I149213910","display_name":"University of Antwerp","ror":"https://ror.org/008x57b05","country_code":"BE","type":"education","lineage":["https://openalex.org/I149213910"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Wen-shin Lee","raw_affiliation_strings":["Universiteit Antwerpen, Belgium"],"affiliations":[{"raw_affiliation_string":"Universiteit Antwerpen, Belgium","institution_ids":["https://openalex.org/I149213910"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057638793"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":4.9366,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.95560037,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9965999722480774,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.6996297240257263},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6146969199180603},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4802025556564331},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4448801279067993},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4201604127883911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4088408946990967},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34202104806900024},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3028010427951813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21899542212486267},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1585829257965088},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08982682228088379}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6996297240257263},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6146969199180603},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4802025556564331},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4448801279067993},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4201604127883911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4088408946990967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34202104806900024},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3028010427951813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21899542212486267},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1585829257965088},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08982682228088379},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1145768.1145792","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145792","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322675","display_name":"Mitacs","ror":"https://ror.org/00cjrc276"},{"id":"https://openalex.org/F4320324595","display_name":"Universiteit Antwerpen","ror":"https://ror.org/008x57b05"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1599026900","https://openalex.org/W1628745019","https://openalex.org/W1791330396","https://openalex.org/W1862515573","https://openalex.org/W1943663571","https://openalex.org/W1963507207","https://openalex.org/W1966287322","https://openalex.org/W1974321539","https://openalex.org/W1979243540","https://openalex.org/W1988452081","https://openalex.org/W1990436029","https://openalex.org/W2001371760","https://openalex.org/W2018522516","https://openalex.org/W2020804487","https://openalex.org/W2021311647","https://openalex.org/W2026111379","https://openalex.org/W2026317840","https://openalex.org/W2030858745","https://openalex.org/W2035352599","https://openalex.org/W2050429600","https://openalex.org/W2069931243","https://openalex.org/W2070279173","https://openalex.org/W2078114900","https://openalex.org/W2086325670","https://openalex.org/W2089240964","https://openalex.org/W2097883065","https://openalex.org/W2113204179","https://openalex.org/W2113291984","https://openalex.org/W2126318803","https://openalex.org/W2127391761","https://openalex.org/W2135359007","https://openalex.org/W2151330691","https://openalex.org/W2170896432","https://openalex.org/W2331226313","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W171076485","https://openalex.org/W190919245","https://openalex.org/W2188428054","https://openalex.org/W2076597547","https://openalex.org/W2133396672","https://openalex.org/W2032816783","https://openalex.org/W4245291382","https://openalex.org/W2007616296","https://openalex.org/W2485420135","https://openalex.org/W2043959303"],"abstract_inverted_index":{"We":[0,60,92],"consider":[1],"the":[2,19,24,43,62,65,72,85,94,101,104,109,118],"problem":[3],"of":[4,7,23,51,80,89,97,103,120],"sparse":[5,68],"interpolation":[6,69],"an":[8],"approximate":[9],"multivariate":[10],"black-box":[11,25],"polynomial":[12,26],"in":[13,35,123],"floating-point":[14],"arithmetic.":[15,40],"That":[16],"is,":[17],"both":[18],"inputs":[20],"and":[21,30,56,71,83,100,128],"outputs":[22],"have":[27],"some":[28],"error,":[29],"all":[31],"numbers":[32],"are":[33],"represented":[34],"standard,":[36],"fixed-precision,":[37],"floating":[38],"point":[39],"By":[41],"interpolating":[42,77],"black":[44],"box":[45],"evaluated":[46],"at":[47],"random":[48],"primitive":[49],"roots":[50],"unity,":[52],"we":[53,116],"give":[54],"efficient":[55],"numerically":[57],"robust":[58],"solutions.":[59],"note":[61],"similarity":[63],"between":[64],"exact":[66],"Ben-Or/Tiwari":[67],"algorithm":[70],"classical":[73],"Prony's":[74,90],"method":[75],"for":[76],"a":[78],"sum":[79],"exponential":[81],"functions,":[82],"exploit":[84],"generalized":[86],"eigenvalue":[87],"reformulation":[88],"method.":[91],"analyze":[93],"numerical":[95,126],"stability":[96],"our":[98,121],"algorithms":[99],"sensitivity":[102],"solutions,":[105],"as":[106,108],"well":[107],"expected":[110],"conditioning":[111],"achieved":[112],"through":[113,125],"randomization.":[114],"Finally,":[115],"demonstrate":[117],"effectiveness":[119],"techniques":[122],"practice":[124],"experiments":[127],"applications.":[129]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
