{"id":"https://openalex.org/W2032671060","doi":"https://doi.org/10.1137/120902914","title":"Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems","display_name":"Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2032671060","doi":"https://doi.org/10.1137/120902914","mag":"2032671060"},"language":"en","primary_location":{"id":"doi:10.1137/120902914","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902914","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-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/A5100341068","display_name":"Nan Li","orcid":"https://orcid.org/0000-0002-6723-0172"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Nan Li","raw_affiliation_strings":["Tianjin University"],"affiliations":[{"raw_affiliation_string":"Tianjin University","institution_ids":["https://openalex.org/I162868743"]}]},{"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/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100341068"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":3.3112,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92108076,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"4","first_page":"1623","last_page":"1640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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":0.9994000196456909,"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/T10142","display_name":"Formal Methods in Verification","score":0.9922999739646912,"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":0.9908999800682068,"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/mathematics","display_name":"Mathematics","score":0.7843872904777527},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6357225775718689},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6099280714988708},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5255835652351379},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5224096775054932},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.5136022567749023},{"id":"https://openalex.org/keywords/wilkinsons-polynomial","display_name":"Wilkinson's polynomial","score":0.43758973479270935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41157156229019165},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2916285991668701},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.20966824889183044},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.13605117797851562}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7843872904777527},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6357225775718689},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6099280714988708},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5255835652351379},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5224096775054932},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.5136022567749023},{"id":"https://openalex.org/C170907076","wikidata":"https://www.wikidata.org/wiki/Q2613931","display_name":"Wilkinson's polynomial","level":5,"score":0.43758973479270935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41157156229019165},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2916285991668701},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.20966824889183044},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.13605117797851562},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120902914","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902914","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W178772886","https://openalex.org/W354883035","https://openalex.org/W1532036648","https://openalex.org/W1605702526","https://openalex.org/W1645810705","https://openalex.org/W1968704649","https://openalex.org/W1972632202","https://openalex.org/W1984396462","https://openalex.org/W1985790586","https://openalex.org/W2005164796","https://openalex.org/W2005318763","https://openalex.org/W2007976113","https://openalex.org/W2009126887","https://openalex.org/W2015721832","https://openalex.org/W2017478419","https://openalex.org/W2026697747","https://openalex.org/W2033936708","https://openalex.org/W2035256983","https://openalex.org/W2036702455","https://openalex.org/W2040076922","https://openalex.org/W2041176477","https://openalex.org/W2053738112","https://openalex.org/W2061965397","https://openalex.org/W2070381457","https://openalex.org/W2071860648","https://openalex.org/W2073664445","https://openalex.org/W2075776392","https://openalex.org/W2077223725","https://openalex.org/W2087518360","https://openalex.org/W2091853326","https://openalex.org/W2101413883","https://openalex.org/W2137286062","https://openalex.org/W2148289821","https://openalex.org/W2168526415","https://openalex.org/W2170345902","https://openalex.org/W2189714409","https://openalex.org/W2283215057","https://openalex.org/W2625794288","https://openalex.org/W4229691908","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2185931218","https://openalex.org/W2028541862","https://openalex.org/W2617044949","https://openalex.org/W4298079332","https://openalex.org/W1523746755","https://openalex.org/W2539190264","https://openalex.org/W2168824908","https://openalex.org/W2047285169","https://openalex.org/W2379877967","https://openalex.org/W3189281032"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"generalize":[4],"the":[5,64,67],"algorithm":[6,68],"described":[7],"by":[8],"Rump":[9],"and":[10,29],"Graillat,":[11],"as":[12,14],"well":[13],"our":[15],"previous":[16],"work":[17],"on":[18,56],"verifying":[19],"breadth-one":[20],"singular":[21,45,73],"solutions":[22,74],"of":[23,66,75],"polynomial":[24,70],"systems,":[25],"to":[26,41,78],"compute":[27],"verified":[28],"narrow":[30],"error":[31,49],"bounds":[32],"such":[33],"that":[34],"a":[35],"slightly":[36],"perturbed":[37],"system":[38],"is":[39,54],"guaranteed":[40],"possess":[42],"an":[43],"isolated":[44],"solution":[46],"within":[47],"computed":[48],"bounds.":[50],"Our":[51],"verification":[52],"method":[53],"based":[55],"deflation":[57],"techniques":[58],"using":[59],"smoothing":[60],"parameters.":[61],"We":[62],"demonstrate":[63],"performance":[65],"for":[69],"systems":[71],"with":[72],"multiplicity":[76],"up":[77],"hundreds.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-03-04T09:10:02.777135","created_date":"2025-10-10T00:00:00"}