{"id":"https://openalex.org/W1577765366","doi":null,"title":"On a Path Following Method for Systems of Equations.","display_name":"On a Path Following Method for Systems of Equations.","publication_year":1979,"publication_date":"1979-07-01","ids":{"openalex":"https://openalex.org/W1577765366","mag":"1577765366"},"language":"en","primary_location":{"id":"pmh:ADA077128","doi":null,"is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA077128","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC AND NTIS","raw_type":"Text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5110126000","display_name":"C. B. Garcia","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. B. Garcia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"T Y Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T Y Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0624,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66855204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9682999849319458,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9682999849319458,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.021299999207258224,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0027000000700354576,"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/path-following","display_name":"path following","score":0.7250000238418579},{"id":"https://openalex.org/keywords/systems-of-equations","display_name":"systems of equations","score":0.7429999709129333},{"id":"https://openalex.org/keywords/predictor-corrector-method","display_name":"predictor-corrector method","score":0.8019999861717224},{"id":"https://openalex.org/keywords/topological-degree-theory","display_name":"topological degree theory","score":0.6060000061988831},{"id":"https://openalex.org/keywords/global-convergence","display_name":"global convergence","score":0.45399999618530273},{"id":"https://openalex.org/keywords/equilibrium-problems","display_name":"equilibrium problems","score":0.628000020980835},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.7789999842643738},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.9110000133514404},{"id":"https://openalex.org/keywords/continuation-method","display_name":"numerical continuation","score":0.4970000088214874}],"concepts":[{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.7554538249969482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6851073503494263},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5060197710990906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43742451071739197},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4224488139152527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24790507555007935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05399027466773987},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:ADA077128","doi":null,"is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA077128","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC AND NTIS","raw_type":"Text"},{"id":"mag:1577765366","doi":null,"is_oa":false,"landing_page_url":"https://apps.dtic.mil/dtic/tr/fulltext/u2/a077128.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7098725274","https://openalex.org/W2143628714","https://openalex.org/W2577920159","https://openalex.org/W86484168","https://openalex.org/W2000649075","https://openalex.org/W2357227876","https://openalex.org/W320109460","https://openalex.org/W594725869","https://openalex.org/W2033129800","https://openalex.org/W1535589357"],"abstract_inverted_index":{"The":[0,35],"problem":[1,47],"of":[2,10,44,53,101,120],"finding":[3],"one":[4],"or":[5,15],"all":[6],"solutions":[7,54],"to":[8,16,38,49,70,78,80,116],"systems":[9,18],"equations,":[11],"equilibrium,":[12],"fixed":[13],"points,":[14],"dynamical":[17],"is":[19,37,63,68,76,91,98,107,123],"considered.":[20],"In":[21,84],"the":[22,56,61,81,95,102,110,114],"last":[23],"few":[24],"years,":[25],"a":[26,41,45,51,87,99],"new":[27],"method":[28,90,111],"has":[29],"emerged":[30],"for":[31,93],"solving":[32],"this":[33,85],"problem.":[34],"idea":[36],"start":[39],"at":[40],"given":[42],"solution":[43],"simpler":[46],"and":[48,75,122],"follow":[50,113],"path":[52,57,67,115],"as":[55],"parameter":[58],"(and":[59],"hence,":[60],"problem)":[62],"gradually":[64],"changed.":[65],"This":[66],"proved":[69],"exist":[71],"via":[72],"topological":[73],"approaches":[74],"shown":[77,108],"lead":[79],"'right'":[82],"place.":[83],"paper,":[86],"general":[88],"predictor-corrector":[89],"described":[92],"following":[94],"curve.":[96],"It":[97,106],"globalization":[100],"classical":[103],"Davidenko":[104],"approach.":[105],"that":[109],"can":[112],"any":[117],"desired":[118],"degree":[119],"accuracy":[121],"convergent.":[124]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}