{"id":"https://openalex.org/W2087518360","doi":"https://doi.org/10.1137/s0036142999361074","title":"Existence Verification for Singular Zeros of Complex Nonlinear Systems","display_name":"Existence Verification for Singular Zeros of Complex Nonlinear Systems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2087518360","doi":"https://doi.org/10.1137/s0036142999361074","mag":"2087518360"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999361074","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361074","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/A5021432838","display_name":"R. Baker Kearfott","orcid":"https://orcid.org/0000-0002-3449-098X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Baker Kearfott","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003694444","display_name":"Jianwei Dian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianwei Dian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055137763","display_name":"Arnold Neumaier","orcid":"https://orcid.org/0000-0002-8328-9641"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Neumaier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021432838"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7476,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.93367799,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"2","first_page":"360","last_page":"379"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8201421499252319},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7446779012680054},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6154244542121887},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5448583960533142},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.51357102394104},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45772844552993774},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45171478390693665},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44518208503723145},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.43192556500434875},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.41213083267211914},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3761199414730072},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3715443015098572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14446526765823364}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8201421499252319},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7446779012680054},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6154244542121887},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5448583960533142},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.51357102394104},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45772844552993774},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45171478390693665},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44518208503723145},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.43192556500434875},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.41213083267211914},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3761199414730072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3715443015098572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14446526765823364},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036142999361074","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361074","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.9853","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.9853","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://interval.louisiana.edu/preprints/2000_degree_from_SIAM.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.41.534","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.534","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://solon.cma.univie.ac.at/~neum/ms/degree.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.8868","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.8868","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://interval.louisiana.edu/preprints/2000_degree_from_SIAM.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W18045698","https://openalex.org/W92559348","https://openalex.org/W157663218","https://openalex.org/W1483874187","https://openalex.org/W1514118425","https://openalex.org/W1569454693","https://openalex.org/W1580809199","https://openalex.org/W1584208430","https://openalex.org/W1607873851","https://openalex.org/W1977804942","https://openalex.org/W1985978629","https://openalex.org/W1992338460","https://openalex.org/W1997422357","https://openalex.org/W2019656110","https://openalex.org/W2023413246","https://openalex.org/W2051942610","https://openalex.org/W2060924166","https://openalex.org/W2066409969","https://openalex.org/W2067648572","https://openalex.org/W2078143896","https://openalex.org/W2090963365","https://openalex.org/W2112417391","https://openalex.org/W2129480103","https://openalex.org/W2137764043","https://openalex.org/W2158490696","https://openalex.org/W2162329857","https://openalex.org/W2170795864","https://openalex.org/W2272795305","https://openalex.org/W2318075236","https://openalex.org/W2570659991","https://openalex.org/W3140445122","https://openalex.org/W3146520007","https://openalex.org/W4210281981","https://openalex.org/W4210916633","https://openalex.org/W4230656725","https://openalex.org/W4234106318","https://openalex.org/W4242871999"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W4251428025"],"abstract_inverted_index":{"Computational":[0],"fixed":[1],"point":[2],"theorems":[3],"can":[4,62,86,107,125,176],"be":[5,63,126,177,215],"used":[6],"to":[7,16,168],"automatically":[8],"verify":[9],"existence":[10,109],"and":[11,110,190,201],"uniqueness":[12],"of":[13,20,31,83,115,121,132,157,171,194,209,218],"a":[14,17,28,123,150,169,180,219],"solution":[15,93,124],"nonlinear":[18],"system":[19,170],"n":[21,24,72,116],"equations":[22,172],"in":[23,45,49,88,94],"variables":[25],"ranging":[26],"within":[27],"given":[29,186],"region":[30],"n-space.":[32],"Such":[33,135],"computations":[34,146],"succeed,":[35],"however,":[36],"only":[37],"when":[38,75],"the":[39,59,69,76,84,95,119,130,141,154,191,210,216],"Jacobi":[40,60,77],"matrix":[41,61,78],"is":[42,79,129,137,163,197,204],"nonsingular":[43],"everywhere":[44],"this":[46,133,188],"region.":[47,160],"However,":[48,112],"problems":[50,54,89],"such":[51,122,145],"as":[52],"bifurcation":[53],"or":[55,65,97],"surface":[56],"intersection":[57],"problems,":[58],"singular,":[64,80],"nearly":[66],"so,":[67],"at":[68],"solution.":[70],"For":[71],"real":[73,211],"variables,":[74,118],"tiny":[81],"perturbations":[82],"problem":[85],"result":[87],"either":[90],"with":[91,98,179],"no":[92,103],"region,":[96],"more":[99],"than":[100],"one;":[101],"thus":[102],"general":[104],"computational":[105],"technique":[106],"prove":[108],"uniqueness.":[111],"for":[113,187,206],"systems":[114],"complex":[117],"multiplicity":[120],"verified.":[127],"That":[128,213],"subject":[131,217],"paper.":[134,221],"verification":[136],"possible":[138,205],"by":[139],"computing":[140],"topological":[142,174],"degree,":[143],"but":[144],"heretofore":[147],"have":[148],"required":[149],"global":[151],"search":[152],"on":[153],"(n-1)-dimensional":[155],"boundary":[156],"an":[158],"n-dimensional":[159],"Here":[161],"it":[162],"observed":[164],"that":[165],"preconditioning":[166],"leads":[167],"whose":[173],"degree":[175],"computed":[178],"much":[181],"lower-dimensional":[182],"search.":[183],"Formulas":[184],"are":[185],"computation,":[189],"special":[192],"case":[193],"rank-defect":[195],"one":[196],"studied,":[198],"both":[199],"theoretically":[200],"empirically.":[202],"Verification":[203],"certain":[207],"subcases":[208],"case.":[212],"will":[214],"companion":[220]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}