{"id":"https://openalex.org/W2133040107","doi":"https://doi.org/10.1145/2442829.2442852","title":"Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values","display_name":"Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W2133040107","doi":"https://doi.org/10.1145/2442829.2442852","mag":"2133040107"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442852","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th 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/A5018201347","display_name":"Matthew T. Comer","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew T. Comer","raw_affiliation_strings":["NCSU Raleigh, NC","NCSU Raleigh, NC#TAB#"],"affiliations":[{"raw_affiliation_string":"NCSU Raleigh, NC","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"NCSU Raleigh, NC#TAB#","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056874049","display_name":"Erich Kaltofen","orcid":"https://orcid.org/0000-0003-2739-3230"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erich L. Kaltofen","raw_affiliation_strings":["NCSU Raleigh, NC","NCSU Raleigh, NC#TAB#"],"affiliations":[{"raw_affiliation_string":"NCSU Raleigh, NC","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"NCSU Raleigh, NC#TAB#","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079752845","display_name":"Cl\u00e9ment Pernet","orcid":"https://orcid.org/0000-0001-6970-0417"},"institutions":[{"id":"https://openalex.org/I177483745","display_name":"Universit\u00e9 Joseph Fourier","ror":"https://ror.org/02aj0kh94","country_code":"FR","type":"education","lineage":["https://openalex.org/I177483745"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Pernet","raw_affiliation_strings":["Universit\u00e9 Joseph Fourier, Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Joseph Fourier, Grenoble, France","institution_ids":["https://openalex.org/I177483745"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018201347"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":5.7459,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.95971398,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"138","last_page":"145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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":0.9991999864578247,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9987999796867371,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"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/outlier","display_name":"Outlier","score":0.7053003907203674},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6974960565567017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6784802675247192},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5627627372741699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5317087769508362},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.5161048173904419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4070884585380554},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.3520705997943878},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21606725454330444},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.05657362937927246}],"concepts":[{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.7053003907203674},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6974960565567017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6784802675247192},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5627627372741699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5317087769508362},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5161048173904419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4070884585380554},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3520705997943878},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21606725454330444},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.05657362937927246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2442829.2442852","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3929551143","display_name":null,"funder_award_id":"ANR-11-BS02-013 (Pernet)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7560107411","display_name":null,"funder_award_id":"CCF-0830347, CCF-1115772","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W58580312","https://openalex.org/W627872862","https://openalex.org/W1587463886","https://openalex.org/W1593683169","https://openalex.org/W1965254799","https://openalex.org/W1977375620","https://openalex.org/W2008095909","https://openalex.org/W2010027455","https://openalex.org/W2018063252","https://openalex.org/W2018522516","https://openalex.org/W2026317840","https://openalex.org/W2028186291","https://openalex.org/W2044993127","https://openalex.org/W2063710137","https://openalex.org/W2065251841","https://openalex.org/W2070279173","https://openalex.org/W2071252649","https://openalex.org/W2082380954","https://openalex.org/W2096282168","https://openalex.org/W2100899126","https://openalex.org/W2116774465","https://openalex.org/W2126318803","https://openalex.org/W2139986679","https://openalex.org/W2148575324","https://openalex.org/W2162442687","https://openalex.org/W2167854544","https://openalex.org/W3117000020","https://openalex.org/W6681722003"],"related_works":["https://openalex.org/W2291214609","https://openalex.org/W2985206855","https://openalex.org/W3183609115","https://openalex.org/W2387056800","https://openalex.org/W2389908107","https://openalex.org/W2108850688","https://openalex.org/W2354295809","https://openalex.org/W1525419764","https://openalex.org/W2532653122","https://openalex.org/W2587745679"],"abstract_inverted_index":{"We":[0],"propose":[1],"algorithms":[2],"performing":[3],"sparse":[4],"interpolation":[5],"with":[6,18],"errors,":[7],"based":[8],"on":[9],"Prony's--Ben-Or's":[10],"&":[11],"Tiwari's":[12],"algorithm,":[13],"using":[14],"a":[15,29,34,84],"Berlekamp/Massey":[16],"algorithm":[17,25,53],"early":[19],"termination.":[20],"First,":[21],"we":[22],"present":[23],"an":[24],"that":[26],"can":[27],"recover":[28],"t-sparse":[30],"polynomial":[31],"f":[32],"from":[33],"sequence":[35],"of":[36,40,68],"values,":[37],"where":[38,63,81],"some":[39],"the":[41,66],"values":[42],"are":[43],"wrong,":[44],"spoiled":[45],"by":[46],"either":[47],"random":[48],"or":[49],"misleading":[50],"errors.":[51,70],"Our":[52],"requires":[54],"bounds":[55],"T":[56],"\u2265":[57,61],"t":[58],"and":[59],"E":[60],"e,":[62],"e":[64],"is":[65,83],"number":[67],"evaluation":[69],"It":[71],"interpolates":[72],"f(\u03c9i)":[73],"for":[74],"i":[75],"=":[76],"1,...,":[77],"2T(E":[78],"+":[79],"1),":[80],"\u03c9":[82],"field":[85],"element":[86],"at":[87],"which":[88],"each":[89],"non-zero":[90],"term":[91],"evaluates":[92],"distinctly.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
