{"id":"https://openalex.org/W4283806842","doi":"https://doi.org/10.1145/3476446.3535501","title":"Sparse Polynomial Hermite Interpolation","display_name":"Sparse Polynomial Hermite Interpolation","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283806842","doi":"https://doi.org/10.1145/3476446.3535501"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3535501","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535501","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 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/A5056874049","display_name":"Erich Kaltofen","orcid":"https://orcid.org/0000-0003-2739-3230"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erich L. Kaltofen","raw_affiliation_strings":["NCSU, Duke University, Raleigh, Durham, NC, USA"],"affiliations":[{"raw_affiliation_string":"NCSU, Duke University, Raleigh, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056874049"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":0.2652,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60053229,"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":"469","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/mathematics","display_name":"Mathematics","score":0.706483006477356},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.674726665019989},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6562149524688721},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.6264665722846985},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5844518542289734},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.5358378291130066},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5069591999053955},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49196669459342957},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4714810848236084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4510558843612671},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4453582763671875},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.43732383847236633},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.42931580543518066},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.42721959948539734},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.4203251600265503},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.19436636567115784},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.17258134484291077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16894876956939697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14462104439735413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1061079204082489},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09796899557113647}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.706483006477356},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.674726665019989},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6562149524688721},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6264665722846985},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5844518542289734},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5358378291130066},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5069591999053955},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49196669459342957},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4714810848236084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4510558843612671},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4453582763671875},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.43732383847236633},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.42931580543518066},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.42721959948539734},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.4203251600265503},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.19436636567115784},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.17258134484291077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16894876956939697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14462104439735413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1061079204082489},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09796899557113647},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3476446.3535501","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3535501","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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/W1973293030","https://openalex.org/W1977375620","https://openalex.org/W2010027455","https://openalex.org/W2026317840","https://openalex.org/W2065660785","https://openalex.org/W2075855683","https://openalex.org/W2126318803","https://openalex.org/W2611959999","https://openalex.org/W2959557165","https://openalex.org/W2962863897","https://openalex.org/W2963820833","https://openalex.org/W2996076570","https://openalex.org/W3090493629","https://openalex.org/W3181810200"],"related_works":["https://openalex.org/W2093301299","https://openalex.org/W2110869895","https://openalex.org/W1576380577","https://openalex.org/W2068749660","https://openalex.org/W2186737732","https://openalex.org/W1991224576","https://openalex.org/W1980267752","https://openalex.org/W426621890","https://openalex.org/W2540879644","https://openalex.org/W4283806842"],"abstract_inverted_index":{"We":[0,97],"present":[1],"Hermite":[2],"polynomial":[3,11,20,31,95],"interpolation":[4],"algorithms":[5,82,99,131],"that":[6,100],"for":[7,45,71,123],"a":[8,16,62,68,110,133],"sparse":[9],"univariate":[10],"f":[12,32],"with":[13,91,138],"coefficients":[14],"from":[15,21,67],"field":[17],"compute":[18],"the":[19,25,29,59,77,105,124],"fewer":[22],"points":[23,106],"than":[24],"classical":[26],"algorithms.":[27],"If":[28,116],"interpolating":[30],"has":[33],"t":[34,48,122],"terms,":[35],"our":[36,130],"algorithms,":[37],"which":[38],"use":[39,132],"randomization,":[40],"require":[41],"argument/value":[42],"triples":[43],"(wi,f(wi),f'(wi))":[44],"i=0,":[46],"...,":[47],"+":[49,142],"\u21be(t+1)/2\u21bf":[50],"-":[51],"1,":[52],"where":[53],"w":[54,136],"is":[55,65,128],"randomly":[56,134],"sampled":[57],"and":[58,89],"probability":[60],"of":[61,79,113,126],"correct":[63,102],"output":[64],"determined":[66],"degree":[69],"bound":[70,119],"f.":[72,80],"With":[73],"f'":[74],"we":[75],"denote":[76],"derivative":[78],"Our":[81],"generalize":[83],"to":[84,93],"multivariate":[85],"polynomials,":[86],"higher":[87],"derivatives":[88],"sparsity":[90],"respect":[92],"Chebyshev":[94],"bases.":[96],"have":[98],"can":[101],"errors":[103],"in":[104],"by":[107],"oversampling":[108],"at":[109],"limited":[111],"number":[112,125],"good":[114],"values.":[115],"an":[117,149],"upper":[118],"B":[120,143],"\u2265":[121],"terms":[127],"given,":[129],"selected":[135],"and,":[137],"high":[139],"probability,":[140],"t/2":[141],"triples,":[144],"but":[145],"then":[146],"never":[147],"return":[148],"incorrect":[150],"output.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
