{"id":"https://openalex.org/W2736521656","doi":"https://doi.org/10.1145/3087604.3087631","title":"Improved Bounds on Absolute Positiveness of Multivariate Polynomials","display_name":"Improved Bounds on Absolute Positiveness of Multivariate Polynomials","publication_year":2017,"publication_date":"2017-07-19","ids":{"openalex":"https://openalex.org/W2736521656","doi":"https://doi.org/10.1145/3087604.3087631","mag":"2736521656"},"language":"en","primary_location":{"id":"doi:10.1145/3087604.3087631","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087631","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM 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/A5070627908","display_name":"Swaroop N. Prabhakar","orcid":null},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Swaroop N. Prabhakar","raw_affiliation_strings":["Institute of Mathematical Sciences, HBNI, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, HBNI, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102371227","display_name":"Vikram Sharma","orcid":null},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vikram Sharma","raw_affiliation_strings":["Institute of Mathematical Sciences, HBNI, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, HBNI, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070627908"],"corresponding_institution_ids":["https://openalex.org/I59611059"],"apc_list":null,"apc_paid":null,"fwci":0.2271,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54669237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"381","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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":0.9977999925613403,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9898999929428101,"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/multivariate-statistics","display_name":"Multivariate statistics","score":0.6231410503387451},{"id":"https://openalex.org/keywords/absolute","display_name":"Absolute (philosophy)","score":0.6095865964889526},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5057470798492432},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.315538227558136},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0663391649723053}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6231410503387451},{"id":"https://openalex.org/C2777487392","wikidata":"https://www.wikidata.org/wiki/Q481201","display_name":"Absolute (philosophy)","level":2,"score":0.6095865964889526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5057470798492432},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.315538227558136},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0663391649723053},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3087604.3087631","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087631","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic 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":19,"referenced_works":["https://openalex.org/W9086223","https://openalex.org/W1496103894","https://openalex.org/W1507039213","https://openalex.org/W1968804058","https://openalex.org/W1972252297","https://openalex.org/W2000929783","https://openalex.org/W2004223891","https://openalex.org/W2082964526","https://openalex.org/W2084232804","https://openalex.org/W2089369436","https://openalex.org/W2096606628","https://openalex.org/W2146291488","https://openalex.org/W2260408687","https://openalex.org/W2474486402","https://openalex.org/W2507569938","https://openalex.org/W2551948348","https://openalex.org/W2565229654","https://openalex.org/W2565903074","https://openalex.org/W2900218551"],"related_works":["https://openalex.org/W2498348907","https://openalex.org/W1979597421","https://openalex.org/W4237736158","https://openalex.org/W2985905814","https://openalex.org/W2007980826","https://openalex.org/W2262959435","https://openalex.org/W4245490552","https://openalex.org/W4229515626","https://openalex.org/W3202488475","https://openalex.org/W4246922841"],"abstract_inverted_index":{"A":[0],"multivariate":[1,135],"polynomial":[2],"F(x1,x2,...,xn)":[3],"is":[4,40,46,91,152],"said":[5],"to":[6,42,76,95,133,164,184],"be":[7,96],"absolutely":[8],"positive":[9],"from":[10],"a":[11,53,73,107,128,138,146,153],"real":[12],"number":[13],"B":[14],"if":[15],"F":[16],"and":[17,81,90,118],"all":[18],"its":[19],"partial":[20],"derivatives":[21],"are":[22],"non-negative":[23],"for":[24],"x1,x2,...,xn":[25],"\u2265":[26],"B.":[27],"One":[28],"of":[29,52,56,63,66,130,140,148,172,179],"the":[30,38,49,60,64,67,70,79,82,86,102,114,134,176,180],"well":[31],"known":[32,182],"bounds":[33],"on":[34,48,120],"absolute":[35,61],"positiveness":[36],"in":[37,85,113],"literature":[39],"due":[41,75],"Hong.":[43],"His":[44],"bound":[45,74,108,132],"dependent":[47],"first":[50,80],"maximum":[51,84],"certain":[54],"sequence":[55,89,117],"radicals":[57],"defined":[58],"using":[59],"value":[62,112],"coefficients":[65],"polynomial.":[68],"In":[69,101,123],"univariate":[71],"setting,":[72],"Lagrange":[77],"considers":[78],"second":[83],"same":[87,115],"radical":[88,116],"shown":[92],"by":[93],"Collins":[94],"better":[97],"than":[98],"Hong's":[99,157,186],"bound.":[100,122,158,168,187],"1930's,":[103],"Westerfield":[104],"had":[105],"proposed":[106],"that":[109],"consides":[110],"every":[111],"improves":[119],"Lagrange's":[121,149],"this":[124,141,166,173],"paper,":[125],"we":[126,143,160],"provide":[127],"generalization":[129,147],"Westerfield's":[131],"setting.":[136],"As":[137],"specialization":[139],"bound,":[142,150],"also":[144],"derive":[145],"which":[151],"strict":[154],"improvement":[155],"upon":[156],"Finally,":[159],"give":[161],"an":[162],"algorithm":[163,174,183],"compute":[165,185],"improved":[167],"The":[169],"running":[170,177],"time":[171,178],"matches":[175],"best":[181]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
