{"id":"https://openalex.org/W1878147714","doi":"https://doi.org/10.1137/140975590","title":"Root Following in Evans Function Computation","display_name":"Root Following in Evans Function Computation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1878147714","doi":"https://doi.org/10.1137/140975590","mag":"1878147714"},"language":"en","primary_location":{"id":"doi:10.1137/140975590","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975590","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/A5085795416","display_name":"Jeffrey Humpherys","orcid":"https://orcid.org/0000-0003-3981-1217"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeffrey Humpherys","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028497099","display_name":"Joshua W. Lytle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joshua Lytle","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085795416"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4658,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87654571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"5","first_page":"2329","last_page":"2346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8014558553695679},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7309666872024536},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.6399949193000793},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5901438593864441},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5436574220657349},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5394713282585144},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5232880711555481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5155877470970154},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44622039794921875},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44162362813949585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1684272289276123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.106302410364151}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014558553695679},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7309666872024536},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.6399949193000793},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5901438593864441},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5436574220657349},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5394713282585144},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5232880711555481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5155877470970154},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44622039794921875},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44162362813949585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1684272289276123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.106302410364151},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140975590","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975590","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W360456325","https://openalex.org/W567289629","https://openalex.org/W1487057719","https://openalex.org/W1533288419","https://openalex.org/W1560060148","https://openalex.org/W1570566316","https://openalex.org/W1854300165","https://openalex.org/W1966747678","https://openalex.org/W1968958624","https://openalex.org/W1976858936","https://openalex.org/W1977085506","https://openalex.org/W1977163495","https://openalex.org/W1977299049","https://openalex.org/W1988664436","https://openalex.org/W1992737652","https://openalex.org/W1994878053","https://openalex.org/W1999873750","https://openalex.org/W2008866196","https://openalex.org/W2017607641","https://openalex.org/W2029662995","https://openalex.org/W2048681097","https://openalex.org/W2051466114","https://openalex.org/W2051965379","https://openalex.org/W2053535383","https://openalex.org/W2056023300","https://openalex.org/W2058579248","https://openalex.org/W2059781860","https://openalex.org/W2059999403","https://openalex.org/W2060018646","https://openalex.org/W2061011795","https://openalex.org/W2062710542","https://openalex.org/W2064184637","https://openalex.org/W2070793107","https://openalex.org/W2073865849","https://openalex.org/W2082428333","https://openalex.org/W2086799845","https://openalex.org/W2088754516","https://openalex.org/W2122531022","https://openalex.org/W2124753825","https://openalex.org/W2126426822","https://openalex.org/W2130123176","https://openalex.org/W2134009775","https://openalex.org/W2144144709","https://openalex.org/W2154913216","https://openalex.org/W2964132234","https://openalex.org/W3105460463"],"related_works":["https://openalex.org/W2146600718","https://openalex.org/W1988099423","https://openalex.org/W2789132480","https://openalex.org/W2987607524","https://openalex.org/W2013562113","https://openalex.org/W3099582283","https://openalex.org/W4291994060","https://openalex.org/W2016834887","https://openalex.org/W155951543","https://openalex.org/W2363941805"],"abstract_inverted_index":{"Evans":[0,118],"function":[1,31,119],"computation":[2],"is":[3,66],"a":[4,77,103],"useful":[5],"tool":[6],"in":[7,19,76],"the":[8,20,34,37,55,59,85,89,94,114,117],"study":[9],"of":[10,22,28,36,58,88,96,116,121],"asymptotically":[11],"constant-coefficient":[12],"linear":[13],"operators":[14],"such":[15],"as":[16,73,80],"those":[17],"found":[18],"investigation":[21],"traveling":[23],"wave":[24],"stability.":[25],"The":[26],"roots":[27,115],"this":[29,99],"analytic":[30],"correspond":[32],"to":[33,62,69,106,112],"eigenvalues":[35,60,72,109],"operator,":[38],"and":[39,45,53,125,131],"by":[40],"employing":[41],"both":[42],"winding":[43,123],"number":[44,124],"root-finding":[46,126],"methods,":[47],"one":[48],"can":[49],"demonstrate":[50],"spectral":[51],"stability":[52],"determine":[54],"precise":[56],"location":[57],"up":[61],"numerical":[63,104],"tolerance.":[64],"It":[65],"often":[67],"desirable":[68],"track":[70,107],"these":[71,108],"parameters":[74],"vary":[75],"system,":[78],"particularly":[79],"they":[81],"may":[82],"cross":[83],"into":[84],"right":[86],"half":[87],"complex":[90],"plane,":[91],"thus":[92],"signaling":[93],"onset":[95],"instability.":[97],"In":[98],"paper,":[100],"we":[101],"present":[102],"method":[105],"using":[110,122],"continuation":[111],"follow":[113],"instead":[120],"techniques,":[127],"therefore":[128],"saving":[129],"time":[130],"effort.":[132],"We":[133],"then":[134],"consider":[135],"some":[136],"examples.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}