{"id":"https://openalex.org/W1993589255","doi":"https://doi.org/10.1137/050624935","title":"Approximate Gauss\u2013Newton Methods for Nonlinear Least Squares Problems","display_name":"Approximate Gauss\u2013Newton Methods for Nonlinear Least Squares Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1993589255","doi":"https://doi.org/10.1137/050624935","mag":"1993589255"},"language":"en","primary_location":{"id":"doi:10.1137/050624935","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624935","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/A5036298459","display_name":"Serge Gratton","orcid":"https://orcid.org/0000-0002-5021-2357"},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Gratton","raw_affiliation_strings":["CERFACS - Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique (42 Avenue Gaspard Coriolis 31057 TOULOUSE CEDEX 1  - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERFACS - Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique (42 Avenue Gaspard Coriolis 31057 TOULOUSE CEDEX 1  - France)","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028604619","display_name":"Amos S. Lawless","orcid":"https://orcid.org/0000-0002-3016-6568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. S. Lawless","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043102786","display_name":"Nancy Nichols","orcid":"https://orcid.org/0000-0003-1133-5220"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. K. Nichols","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3583,"has_fulltext":false,"cited_by_count":240,"citation_normalized_percentile":{"value":0.91372591,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"18","issue":"1","first_page":"106","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8368973731994629},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.6325843334197998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5946811437606812},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5926242470741272},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5775874853134155},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5322036147117615},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.5218388438224792},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.5135400295257568},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5039069056510925},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48914459347724915},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.4780302941799164},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.4580248296260834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4556584060192108},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4061627686023712},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26316532492637634},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.10129398107528687}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8368973731994629},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.6325843334197998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5946811437606812},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5926242470741272},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5775874853134155},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5322036147117615},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.5218388438224792},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.5135400295257568},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5039069056510925},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48914459347724915},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.4780302941799164},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.4580248296260834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4556584060192108},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4061627686023712},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26316532492637634},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.10129398107528687},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.0},{"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/050624935","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624935","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:10.1.1.224.7161","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.7161","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.reading.ac.uk/web/FILES/maths/09-04.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03707467v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03707467","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1052-6234","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:centaur.reading.ac.uk:875","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/875/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","score":0.8799999952316284,"display_name":"Life below water"}],"awards":[{"id":"https://openalex.org/G295385014","display_name":null,"funder_award_id":"NE/E002048/1","funder_id":"https://openalex.org/F4320320022","funder_display_name":"Sight Research UK"},{"id":"https://openalex.org/G6626006868","display_name":null,"funder_award_id":"NE/E002048/1","funder_id":"https://openalex.org/F4320334631","funder_display_name":"Natural Environment Research Council"}],"funders":[{"id":"https://openalex.org/F4320320022","display_name":"Sight Research UK","ror":"https://ror.org/03z2py885"},{"id":"https://openalex.org/F4320334631","display_name":"Natural Environment Research Council","ror":"https://ror.org/02b5d8509"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W13042550","https://openalex.org/W68750926","https://openalex.org/W1487655136","https://openalex.org/W1523222099","https://openalex.org/W1965573563","https://openalex.org/W1971947347","https://openalex.org/W1980138760","https://openalex.org/W1992112074","https://openalex.org/W1998780272","https://openalex.org/W2010315317","https://openalex.org/W2052803362","https://openalex.org/W2052827274","https://openalex.org/W2068484625","https://openalex.org/W2090963365","https://openalex.org/W2093756001","https://openalex.org/W2096245308","https://openalex.org/W2107501462","https://openalex.org/W2132753583","https://openalex.org/W2138513194","https://openalex.org/W2139004160","https://openalex.org/W2170391029","https://openalex.org/W2478091498"],"related_works":["https://openalex.org/W2983297293","https://openalex.org/W4388964614","https://openalex.org/W2972343833","https://openalex.org/W2996136316","https://openalex.org/W2970432723","https://openalex.org/W1560140409","https://openalex.org/W2082821409","https://openalex.org/W2889643804","https://openalex.org/W2463007134","https://openalex.org/W2142947426"],"abstract_inverted_index":{"The":[0,38,212],"Gauss\u2013Newton":[1,98,138,154,172,200],"algorithm":[2,74],"is":[3,16,56,75,100,163,180,235],"an":[4,59],"iterative":[5,63],"method":[6,69,99,139],"regularly":[7],"used":[8,145],"for":[9,209],"solving":[10],"nonlinear":[11,51],"least":[12,46,160,188],"squares":[13,47,161,189],"problems.":[14],"It":[15],"particularly":[17],"well":[18],"suited":[19],"to":[20,49,103,116,121,224],"the":[21,50,73,82,88,91,96,123,131,134,137,157,175,196,210,225],"treatment":[22],"of":[23,41,44,54,84,90,136,140,143,207,227],"very":[24],"large":[25],"scale":[26],"variational":[27],"data":[28,148,228],"assimilation":[29,229],"problems":[30,124],"that":[31,195],"arise":[32],"in":[33,87,106,114,125,147,230],"atmosphere":[34],"and":[35,70,109,120,167,198,203],"ocean":[36],"forecasting.":[37],"procedure":[39],"consists":[40],"a":[42,183,217,231],"sequence":[43],"linear":[45,159,187],"approximations":[48,111],"problem,":[52],"each":[53],"which":[55],"solved":[57,165],"by":[58,182,216],"\u201cinner\u201d":[60],"direct":[61],"or":[62,185],"process.":[64],"In":[65,94],"comparison":[66],"with":[67],"Newton\u2019s":[68],"its":[71],"variants,":[72],"attractive":[76],"because":[77],"it":[78],"does":[79],"not":[80,164],"require":[81],"evaluation":[83],"second\u2010order":[85],"derivatives":[86],"Hessian":[89],"objective":[92],"function.":[93],"practice":[95],"exact":[97],"too":[101],"expensive":[102],"apply":[104],"operationally":[105],"meteorological":[107,233],"forecasting,":[108],"various":[110],"are":[112,214],"made":[113],"order":[115],"reduce":[117],"computational":[118],"costs":[119],"solve":[122],"real":[126],"time.":[127],"Here":[128],"we":[129,151,169],"investigate":[130],"effects":[132],"on":[133],"convergence":[135,208],"two":[141],"types":[142],"approximation":[144],"commonly":[146],"assimilation.":[149],"First,":[150],"examine":[152,170],"\u201ctruncated\u201d":[153],"methods":[155,173,201],"where":[156,174],"inner":[158,178],"problem":[162,179,226],"exactly,":[166],"second,":[168],"\u201cperturbed\u201d":[171],"true":[176],"linearized":[177],"approximated":[181],"simplified,":[184],"perturbed,":[186],"problem.":[190],"We":[191],"give":[192],"conditions":[193],"ensuring":[194],"truncated":[197],"perturbed":[199],"converge":[202],"also":[204],"derive":[205],"rates":[206],"iterations.":[211],"results":[213],"illustrated":[215],"simple":[218],"numerical":[219],"example.":[220],"A":[221],"practical":[222],"application":[223],"typical":[232],"system":[234],"presented.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":24},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
