{"id":"https://openalex.org/W2062754393","doi":"https://doi.org/10.1007/s11075-011-9463-8","title":"Efficient path tracking methods","display_name":"Efficient path tracking methods","publication_year":2011,"publication_date":"2011-04-19","ids":{"openalex":"https://openalex.org/W2062754393","doi":"https://doi.org/10.1007/s11075-011-9463-8","mag":"2062754393"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-011-9463-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-011-9463-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5089126031","display_name":"Daniel J. Bates","orcid":"https://orcid.org/0000-0003-2985-0554"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel J. Bates","raw_affiliation_strings":["Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA","Department of Mathematics, Colorado State University, Fort Collins, USA 80523#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, USA 80523#TAB#","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007214938","display_name":"Jonathan D. Hauenstein","orcid":"https://orcid.org/0000-0002-9252-8210"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan D. Hauenstein","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Mailstop 3368, TX, 77843, USA","Department of Mathematics, Texas A&M University, College Station, TX, USA 77843"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Mailstop 3368, TX, 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA 77843","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103556278","display_name":"Andrew J. Sommese","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Sommese","raw_affiliation_strings":["Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA","Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA 46556#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA 46556#TAB#","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089126031"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.9032,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.93798164,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"58","issue":"4","first_page":"451","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9995999932289124,"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":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9937000274658203,"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/theory-of-computation","display_name":"Theory of computation","score":0.6676510572433472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6164337992668152},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5720215439796448},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5567935705184937},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5164344906806946},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5143764615058899},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.5048769116401672},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49875497817993164},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.48657238483428955},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.47100749611854553},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46031850576400757},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4432113766670227},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40018725395202637},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38411882519721985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37952500581741333},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3331359624862671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3224932551383972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10803508758544922},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09273657202720642}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6676510572433472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6164337992668152},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5720215439796448},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5567935705184937},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5164344906806946},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5143764615058899},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5048769116401672},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49875497817993164},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.48657238483428955},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.47100749611854553},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46031850576400757},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4432113766670227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40018725395202637},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38411882519721985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37952500581741333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3331359624862671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3224932551383972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10803508758544922},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09273657202720642},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-011-9463-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-011-9463-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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":20,"referenced_works":["https://openalex.org/W368072353","https://openalex.org/W421502599","https://openalex.org/W1570420806","https://openalex.org/W1676198905","https://openalex.org/W1968559856","https://openalex.org/W1969122636","https://openalex.org/W2061376823","https://openalex.org/W2066409969","https://openalex.org/W2067437385","https://openalex.org/W2085471512","https://openalex.org/W2088986191","https://openalex.org/W2132476962","https://openalex.org/W2139482396","https://openalex.org/W2167360454","https://openalex.org/W2170485468","https://openalex.org/W2997123088","https://openalex.org/W4241062739","https://openalex.org/W4247101350","https://openalex.org/W4292929576","https://openalex.org/W4298231803"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4248087735","https://openalex.org/W4225310406","https://openalex.org/W4229560034","https://openalex.org/W2039023896","https://openalex.org/W2028790718"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}