{"id":"https://openalex.org/W2011529154","doi":"https://doi.org/10.1137/040604029","title":"Inexact Newton Regularization Using Conjugate Gradients as Inner Iteration","display_name":"Inexact Newton Regularization Using Conjugate Gradients as Inner Iteration","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2011529154","doi":"https://doi.org/10.1137/040604029","mag":"2011529154"},"language":"en","primary_location":{"id":"doi:10.1137/040604029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040604029","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5445/ir/1000011041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058851181","display_name":"Andreas Rieder","orcid":"https://orcid.org/0000-0002-3192-2847"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Rieder","raw_affiliation_strings":["Institut f\u00fcr Praktische Mathematik und Institut f\u00fcr Wissenschaftliches Rechnen und Mathe-matische Modellbildung, Universit\u00e4t Karlsruhe, 76128 Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Praktische Mathematik und Institut f\u00fcr Wissenschaftliches Rechnen und Mathe-matische Modellbildung, Universit\u00e4t Karlsruhe, 76128 Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058851181"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":2.0346,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.84076208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"604","last_page":"622"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9944999814033508,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9940999746322632,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.8653084635734558},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8270134925842285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8001848459243774},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6533448696136475},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6526877284049988},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5328699946403503},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5012938976287842},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4920153319835663},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.486162394285202},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48338714241981506},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48167312145233154},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.44076472520828247},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.43152594566345215},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.4171365201473236},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3561476767063141},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2784118056297302},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.18379810452461243},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0978429913520813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0945080816745758},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05913016200065613}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.8653084635734558},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8270134925842285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8001848459243774},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6533448696136475},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6526877284049988},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5328699946403503},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5012938976287842},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4920153319835663},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.486162394285202},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48338714241981506},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48167312145233154},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.44076472520828247},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.43152594566345215},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.4171365201473236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3561476767063141},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2784118056297302},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.18379810452461243},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0978429913520813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0945080816745758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05913016200065613},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040604029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040604029","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"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000011041","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000011041","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis, 73 (2), 604-622","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.5445/ir/1000011041","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000011041","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5445/ir/1000011041","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000011041","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W4965458","https://openalex.org/W1542744440","https://openalex.org/W1570089119","https://openalex.org/W2017714771","https://openalex.org/W2019847820","https://openalex.org/W2022097729","https://openalex.org/W2025056020","https://openalex.org/W2047211871","https://openalex.org/W2080888649","https://openalex.org/W2081774672","https://openalex.org/W2085314413","https://openalex.org/W2480154215","https://openalex.org/W2488131745","https://openalex.org/W4235485079"],"related_works":["https://openalex.org/W2098528027","https://openalex.org/W2005717169","https://openalex.org/W3159557833","https://openalex.org/W2183734858","https://openalex.org/W3159907817","https://openalex.org/W4319027779","https://openalex.org/W2941778027","https://openalex.org/W2060532089","https://openalex.org/W3194092090","https://openalex.org/W7156132"],"abstract_inverted_index":{"In":[0,88],"our":[1],"papers":[2,71],"[Inverse":[3],"Problems,":[4],"15":[5],"(1999),":[6],"pp.":[7,14,138],"309--327]":[8],"and":[9,51,85],"[Numer.":[10,132],"Math.,":[11],"88":[12],"(2001),":[13],"347--365]":[15],"we":[16,92,112,143],"proposed":[17],"algorithm":[18],"{\\tt":[19,32,97,124],"REGINN},":[20],"an":[21,52],"inexact":[22],"Newton":[23,44,58],"iteration":[24,45],"for":[25,96],"the":[26,38,48,57,62,89,100,128,146,151],"stable":[27],"solution":[28],"of":[29,35,118],"nonlinear":[30],"ill-posedproblems.":[31],"REGINN}":[33,98,125],"consists":[34],"two":[36],"components:":[37],"outer":[39],"iteration,":[40,54,80,83],"which":[41,55,104],"is":[42,105],"a":[43,115],"stopped":[46],"by":[47,60],"discrepancy":[49],"principle,":[50],"inner":[53,79,109,154],"computes":[56],"correction":[59],"solving":[61],"linearized":[63],"system.":[64],"The":[65],"convergence":[66,94,116],"analysis":[67,117],"presented":[68],"in":[69],"both":[70],"covers":[72],"virtually":[73],"any":[74],"linear":[75],"regularization":[76],"method":[77,131,149],"as":[78,108,153],"especially":[81],"Landweber":[82],"$\\nu$-methods,":[84],"Tikhonov--Phillips":[86],"regularization.":[87],"present":[90],"paper":[91],"prove":[93],"rates":[95],"when":[99],"conjugate":[101,129,147],"gradient":[102,130,148],"method,":[103],"nonlinear,":[106],"serves":[107],"iteration.":[110,155],"Thereby":[111],"add":[113],"to":[114],"{Hanke},":[119],"who":[120],"had":[121],"previously":[122],"investigated":[123],"furnished":[126],"with":[127],"Funct.":[133],"Anal.":[134],"Optim.,":[135],"18":[136],"(1997),":[137],"971--993].":[139],"By":[140],"numerical":[141],"experiments":[142],"illustrate":[144],"that":[145],"outperforms":[150],"$\\nu$-method":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
