{"id":"https://openalex.org/W2154406034","doi":"https://doi.org/10.1145/1837934.1837979","title":"Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method","display_name":"Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2154406034","doi":"https://doi.org/10.1145/1837934.1837979","mag":"2154406034"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837979","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 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/A5053194336","display_name":"Sharon Hutton","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":false,"raw_author_name":"Sharon Hutton","raw_affiliation_strings":["NCSU Raleigh, North Carolina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NCSU Raleigh, North Carolina","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, North Carolina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NCSU Raleigh, North Carolina","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["Key Laboratory of Mathematics Mechanization, AMSS, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics Mechanization, AMSS, Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7177,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85220928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"227","last_page":"234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.6699217557907104},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6387485861778259},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.6303278803825378},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.5523496270179749},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5401133298873901},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5117354393005371},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5016233921051025},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4641132950782776},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4159208834171295},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.41023704409599304},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3246085047721863},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2157769799232483},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20871487259864807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11075302958488464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6699217557907104},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6387485861778259},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6303278803825378},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.5523496270179749},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5401133298873901},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5117354393005371},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5016233921051025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4641132950782776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4159208834171295},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.41023704409599304},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3246085047721863},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2157769799232483},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20871487259864807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11075302958488464},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1837934.1837979","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.175.6437","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.6437","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www4.ncsu.edu/%7Ekaltofen/bibliography/10/HKZ10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6100000143051147,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1571220144","display_name":null,"funder_award_id":"60821002/F026091113036910871194","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4829543606","display_name":null,"funder_award_id":"CCF-0830347CCF-0514585DMS-0532140OISE-0913588","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G829543611","display_name":null,"funder_award_id":"CCF-0830347CCF-0514585DMS-0532140OISE-0913588","funder_id":"https://openalex.org/F4320337370","funder_display_name":"Office of International Science and Engineering"},{"id":"https://openalex.org/G8318587132","display_name":null,"funder_award_id":"CCF-0830347CCF-0514585DMS-0532140OISE-0913588","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337370","display_name":"Office of International Science and Engineering","ror":"https://ror.org/01k638r21"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W29697380","https://openalex.org/W261423654","https://openalex.org/W1592751003","https://openalex.org/W1967073510","https://openalex.org/W1967980374","https://openalex.org/W1971521743","https://openalex.org/W1982216340","https://openalex.org/W1984804592","https://openalex.org/W1990436029","https://openalex.org/W1995320256","https://openalex.org/W2007391649","https://openalex.org/W2011703168","https://openalex.org/W2016389104","https://openalex.org/W2027267671","https://openalex.org/W2028594942","https://openalex.org/W2060143865","https://openalex.org/W2065337617","https://openalex.org/W2078605119","https://openalex.org/W2093269606","https://openalex.org/W2094643212","https://openalex.org/W2153451837","https://openalex.org/W2154155820","https://openalex.org/W2318268489","https://openalex.org/W2321177036","https://openalex.org/W2498144272","https://openalex.org/W2536620281","https://openalex.org/W2751335644","https://openalex.org/W2773345027","https://openalex.org/W2952988128","https://openalex.org/W3183392806","https://openalex.org/W4252892841","https://openalex.org/W6744242987"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W2033213447","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W37157938"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,38],"stability":[3],"criterion":[4],"for":[5],"real":[6],"polynomial":[7,33],"inequalities":[8,55],"with":[9],"floating":[10],"point":[11],"or":[12,19],"inexact":[13],"scalars":[14],"by":[15],"estimating":[16],"from":[17],"below":[18],"computing":[20],"the":[21,28,32,45,54],"radius":[22,26,51],"of":[23,31],"semidefiniteness.":[24],"That":[25],"is":[27],"maximum":[29],"deformation":[30],"coefficient":[34],"vector":[35,41],"measured":[36],"in":[37],"weighted":[39],"Euclidean":[40],"norm":[42],"within":[43],"which":[44],"inequality":[46],"remains":[47],"true.":[48],"A":[49],"large":[50],"means":[52],"that":[53],"may":[56],"be":[57],"considered":[58],"numerically":[59],"valid.":[60]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
