{"id":"https://openalex.org/W2026909646","doi":"https://doi.org/10.1145/1277500.1277525","title":"Computing Approximate GCDs in Ill-conditioned Cases","display_name":"Computing Approximate GCDs in Ill-conditioned Cases","publication_year":2007,"publication_date":"2007-07-25","ids":{"openalex":"https://openalex.org/W2026909646","doi":"https://doi.org/10.1145/1277500.1277525","mag":"2026909646"},"language":"en","primary_location":{"id":"doi:10.1145/1277500.1277525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277525","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international workshop on Symbolic-numeric computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5026419015","display_name":"Masaru Sanuki","orcid":"https://orcid.org/0000-0003-4247-539X"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masaru Sanuki","raw_affiliation_strings":["University of Tsukuba, Tsukuba-Shi, Ibaraki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba-Shi, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110109692","display_name":"Tateaki Sasaki","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tateaki Sasaki","raw_affiliation_strings":["University of Tsukuba, Tsukuba-Shi, Ibaraki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba-Shi, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I146399215"],"apc_list":null,"apc_paid":null,"fwci":1.6453,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83029772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"170","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987000226974487,"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":0.9987000226974487,"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/T11697","display_name":"Numerical Methods and Algorithms","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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.870466947555542},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6021890640258789},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4417068660259247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43597257137298584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.419845849275589},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4191874563694},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37503498792648315},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.27843743562698364}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.870466947555542},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6021890640258789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4417068660259247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43597257137298584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.419845849275589},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4191874563694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37503498792648315},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27843743562698364},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277500.1277525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277525","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international workshop on Symbolic-numeric computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W187097693","https://openalex.org/W1591544103","https://openalex.org/W1602290632","https://openalex.org/W1967467218","https://openalex.org/W1988486072","https://openalex.org/W1990436029","https://openalex.org/W1997254026","https://openalex.org/W2026909646","https://openalex.org/W2036031713","https://openalex.org/W2042319052","https://openalex.org/W2049417271","https://openalex.org/W2055292813","https://openalex.org/W2060143865","https://openalex.org/W2061311874","https://openalex.org/W2066621894","https://openalex.org/W2068937275","https://openalex.org/W2069065624","https://openalex.org/W2077315987","https://openalex.org/W2117535139","https://openalex.org/W2127391761","https://openalex.org/W2130331374","https://openalex.org/W2137868850","https://openalex.org/W3151570429"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2049578243","https://openalex.org/W2000145235","https://openalex.org/W2122079181","https://openalex.org/W1985848810","https://openalex.org/W2889939530","https://openalex.org/W3121881699","https://openalex.org/W2748838164","https://openalex.org/W2066015000","https://openalex.org/W2912721996"],"abstract_inverted_index":{"The":[0,40,59],"ill-conditioned":[1],"cases":[2],"we":[3,80],"consider":[4],"are":[5,65],"1)":[6],"the":[7,34,46,51,62,68,71,90,100],"small":[8,12,56],"leading-coefficient":[9,13,25],"case,":[10,15,20],"2)":[11],"GCD":[14],"3)":[16],"big":[17],"leading":[18,57],"coefficient":[19],"and":[21,61,70,103],"4)":[22],"approximately":[23],"singular":[24],"case.":[26],"We":[27],"propose":[28,81],"three":[29],"new":[30],"algorithms":[31,98],"for":[32,76],"computing":[33],"approximate":[35],"GCDs":[36],"in":[37],"these":[38],"cases.":[39],"first":[41],"one":[42],"is":[43],"to":[44,84],"stabilize":[45],"univariate":[47],"PRS":[48],"by":[49,53],"avoiding":[50],"division":[52],"polynomials":[54],"of":[55,67],"coefficients.":[58],"second":[60],"third":[63],"ones":[64],"modifications":[66],"QRGCD":[69],"(approximate)":[72],"PC-PRS":[73],"methods,":[74],"respectively,":[75],"multivariate":[77],"polynomials.":[78],"Furthermore,":[79],"a":[82],"device":[83],"remove":[85,99],"fully-erroneous":[86],"terms":[87],"arising":[88],"from":[89],"exact":[91],"cancellation.":[92],"Some":[93],"experiments":[94],"show":[95],"that":[96],"our":[97],"instability":[101],"considerably":[102],"work":[104],"quite":[105],"efficiently.":[106]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}