{"id":"https://openalex.org/W2027049625","doi":"https://doi.org/10.1145/1390768.1390808","title":"The nearest polynomial with a zero in a given domain from a geometrical viewpoint","display_name":"The nearest polynomial with a zero in a given domain from a geometrical viewpoint","publication_year":2008,"publication_date":"2008-07-20","ids":{"openalex":"https://openalex.org/W2027049625","doi":"https://doi.org/10.1145/1390768.1390808","mag":"2027049625"},"language":"en","primary_location":{"id":"doi:10.1145/1390768.1390808","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390768.1390808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first international symposium on Symbolic and algebraic 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/A5021311433","display_name":"Hiroshi Sekigawa","orcid":"https://orcid.org/0009-0003-1770-0994"},"institutions":[{"id":"https://openalex.org/I2251713219","display_name":"NTT (Japan)","ror":"https://ror.org/00berct97","country_code":"JP","type":"company","lineage":["https://openalex.org/I2251713219"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroshi Sekigawa","raw_affiliation_strings":["Nippon Telegraph and Telephone Corporation, Atsugi-shi, Japan","Nippon Telegraph and Telephone Corporation, Atsugi-shi, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nippon Telegraph and Telephone Corporation, Atsugi-shi, Japan","institution_ids":["https://openalex.org/I2251713219"]},{"raw_affiliation_string":"Nippon Telegraph and Telephone Corporation, Atsugi-shi, Japan#TAB#","institution_ids":["https://openalex.org/I2251713219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021311433"],"corresponding_institution_ids":["https://openalex.org/I2251713219"],"apc_list":null,"apc_paid":null,"fwci":1.7111,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84164892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"287","last_page":"294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983000159263611,"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":0.9983000159263611,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9940000176429749,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/piecewise","display_name":"Piecewise","score":0.8519222736358643},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.7564508318901062},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.7519552707672119},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.7478978037834167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7379408478736877},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6713693141937256},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5913789868354797},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5397828817367554},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5051248669624329},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.44934284687042236},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42002102732658386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32582926750183105},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.07695022225379944},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07091471552848816}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8519222736358643},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7564508318901062},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7519552707672119},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7478978037834167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7379408478736877},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6713693141937256},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5913789868354797},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5397828817367554},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5051248669624329},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44934284687042236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42002102732658386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32582926750183105},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.07695022225379944},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07091471552848816},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1390768.1390808","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390768.1390808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first 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":18,"referenced_works":["https://openalex.org/W1574669531","https://openalex.org/W1966641819","https://openalex.org/W1984804592","https://openalex.org/W2014467673","https://openalex.org/W2027267671","https://openalex.org/W2028747718","https://openalex.org/W2039879619","https://openalex.org/W2065337617","https://openalex.org/W2071852476","https://openalex.org/W2078605119","https://openalex.org/W2088353167","https://openalex.org/W2110187092","https://openalex.org/W2134114550","https://openalex.org/W2137081319","https://openalex.org/W2320799707","https://openalex.org/W2753704026","https://openalex.org/W3143535630","https://openalex.org/W4290864872"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W2059826422"],"abstract_inverted_index":{"For":[0],"a":[1,7,16,21,26,33,42,65,72,91,96,112],"real":[2,34,78],"univariate":[3,22,35],"polynomial":[4,36],"f":[5,37,40,61],"and":[6,46,62,79,116],"closed":[8],"complex":[9],"domain":[10],"D,":[11],"whose":[12],"boundary":[13],"C":[14,70,115],"is":[15,29,50,54,71,90],"simple":[17],"curve":[18],"parameterized":[19],"by":[20,105],"piecewise":[23,73,92],"rational":[24,74,93],"function,":[25],"rigorous":[27],"method":[28],"given":[30],"for":[31],"finding":[32],"such":[38],"that":[39,56,109],"has":[41,111],"zero":[43,66,113],"in":[44,69],"D":[45],"|f":[47],"-":[48],"~f|\u221e":[49],"minimal.":[51],"First,":[52],"it":[53],"proved":[55],"the":[57,77,87,100,107,118],"minimum":[58,88,119],"distance":[59,89,120],"between":[60],"polynomials":[63],"having":[64],"at":[67],"\u03b1":[68],"function":[75,94],"of":[76,82,95,102],"imaginary":[80],"parts":[81],"\u03b1.":[83],"Thus,":[84],"on":[85,114,121],"C,":[86,122],"parameter":[97],"obtained":[98],"through":[99],"parameterization":[101],"C.":[103],"Therefore,":[104],"using":[106],"property":[108],"~f":[110,123],"computing":[117],"can":[124],"be":[125],"constructed.":[126]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}