{"id":"https://openalex.org/W2079440004","doi":"https://doi.org/10.1137/0804022","title":"Globally Convergent Inexact Newton Methods","display_name":"Globally Convergent Inexact Newton Methods","publication_year":1994,"publication_date":"1994-05-01","ids":{"openalex":"https://openalex.org/W2079440004","doi":"https://doi.org/10.1137/0804022","mag":"2079440004"},"language":"en","primary_location":{"id":"doi:10.1137/0804022","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804022","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","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/A5110701881","display_name":"Stanley C. Eisenstat","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stanley C. Eisenstat","raw_affiliation_strings":["Department of Computer Science and Research Center for Scientific Computation, Yale Uni-versity, P. O. Box 2158, New Haven, Connecticut 06520"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Research Center for Scientific Computation, Yale Uni-versity, P. O. Box 2158, New Haven, Connecticut 06520","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049591038","display_name":"Homer F. Walker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Homer F. Walker","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110701881"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":14.7801,"has_fulltext":false,"cited_by_count":445,"citation_normalized_percentile":{"value":0.99479167,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"4","issue":"2","first_page":"393","last_page":"422"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9990000128746033,"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":0.9990000128746033,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944000244140625,"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":0.8287451267242432},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7836658954620361},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7364374399185181},{"id":"https://openalex.org/keywords/newton-fractal","display_name":"Newton fractal","score":0.7163170576095581},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.6880841255187988},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.617794394493103},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5955674648284912},{"id":"https://openalex.org/keywords/steffensens-method","display_name":"Steffensen's method","score":0.588869035243988},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.534162163734436},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5290469527244568},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.49689987301826477},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47830989956855774},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.46540218591690063},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.4455903172492981},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.44223538041114807},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.30250999331474304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.270710825920105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2386946976184845},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16090211272239685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10027462244033813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09280911087989807},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.05972650647163391}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8287451267242432},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7836658954620361},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7364374399185181},{"id":"https://openalex.org/C194342247","wikidata":"https://www.wikidata.org/wiki/Q1151001","display_name":"Newton fractal","level":4,"score":0.7163170576095581},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.6880841255187988},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.617794394493103},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5955674648284912},{"id":"https://openalex.org/C173443657","wikidata":"https://www.wikidata.org/wiki/Q7606635","display_name":"Steffensen's method","level":5,"score":0.588869035243988},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.534162163734436},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5290469527244568},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.49689987301826477},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47830989956855774},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.46540218591690063},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.4455903172492981},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.44223538041114807},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.30250999331474304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.270710825920105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2386946976184845},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16090211272239685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10027462244033813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09280911087989807},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.05972650647163391},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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":2,"locations":[{"id":"doi:10.1137/0804022","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804022","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.573.3921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.573.3921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.wpi.edu/~walker/Papers/global_inexact_newton,SIOPT_4,1994,393-422.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G5219260752","display_name":null,"funder_award_id":"DE-FG","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309198","display_name":"Utah State University","ror":"https://ror.org/00h6set76"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W275685090","https://openalex.org/W1528063838","https://openalex.org/W1550543785","https://openalex.org/W1600159612","https://openalex.org/W1969800610","https://openalex.org/W1969811075","https://openalex.org/W1978562552","https://openalex.org/W1988849934","https://openalex.org/W1996723024","https://openalex.org/W2012960907","https://openalex.org/W2068484625","https://openalex.org/W2075184363","https://openalex.org/W2090963365","https://openalex.org/W2107501462","https://openalex.org/W2140153041","https://openalex.org/W2159336103","https://openalex.org/W3118870036","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2387535608","https://openalex.org/W2031390949","https://openalex.org/W2340363276","https://openalex.org/W4200295560","https://openalex.org/W1518402494","https://openalex.org/W3001734434","https://openalex.org/W2360024674","https://openalex.org/W2079440004","https://openalex.org/W2808820944","https://openalex.org/W2353652015"],"abstract_inverted_index":{"Abstract.":[0],"Inexact":[1],"Newton":[2,26,42,109,155,176,181,183,187],"methods":[3,43,200],"for":[4,198],"finding":[5],"a":[6,60,75,80,93],"zero":[7],"of":[8,14,33,38,77,132,165],"F":[9,85],"1":[10,11],"are":[12,44,111],"variations":[13],"Newton\u2019s":[15,133,167,189],"method":[16,168],"in":[17],"which":[18,84],"each":[19,58],"step":[20],"only":[21],"approximately":[22],"satisfies":[23],"the":[24,31,34,68,96,114,118,130,137],"linear":[25,36,139],"equation":[27],"but":[28,157],"still":[29],"reduces":[30],"norm":[32],"local":[35],"model":[37],"F.":[39],"Here,":[40],"inexact":[41,108,154,175,180],"formulated":[45],"that":[46,89,106,169],"incorporate":[47],"features":[48],"designed":[49],"to":[50,67,99,129,141,149,162],"improve":[51],"convergence":[52,63,119,196],"from":[53],"arbitrary":[54],"starting":[55],"points.":[56],"For":[57],"method,":[59,134,190],"basic":[61],"global":[62,195],"result":[64],"is":[65,86,92,104,148,159],"established":[66],"effect":[69],"that,":[70],"under":[71],"reasonable":[72],"assump-tions,":[73],"if":[74],"sequence":[76,97],"iterates":[78],"has":[79],"limit":[81,90],"point":[82,91],"at":[83],"invertible,":[87],"then":[88],"solution":[94],"and":[95,116,151],"converges":[98],"it.":[100],"When":[101],"appropriate,":[102],"it":[103],"shown":[105],"initial":[107,138],"steps":[110],"taken":[112],"near":[113],"solution,":[115],"so":[117],"can":[120,170],"ultimately":[121],"be":[122,142,172],"made":[123],"as":[124,126,174],"fast":[125],"desired,":[127],"up":[128],"rate":[131],"by":[135],"forcing":[136],"residuals":[140],"appropriately":[143],"small.":[144],"The":[145],"primary":[146],"goal":[147],"introduce":[150],"analyze":[152],"new":[153],"methods,":[156,182,185,188,194],"consideration":[158],"also":[160],"given":[161],"&amp;quot;globalizations":[163],"&amp;quot;":[164],"(exact)":[166],"naturally":[171],"viewed":[173],"methods.":[177],"Key":[178],"words,":[179],"iterative":[184],"truncated":[186],"globally":[191],"convergent":[192],"Newton-like":[193,199],"analyses":[197],"AMS":[201],"subject":[202],"classification.":[203],"65H10":[204]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":22},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
