{"id":"https://openalex.org/W1993251277","doi":"https://doi.org/10.1137/040611653","title":"On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method","display_name":"On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1993251277","doi":"https://doi.org/10.1137/040611653","mag":"1993251277"},"language":"en","primary_location":{"id":"doi:10.1137/040611653","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611653","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"],"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/A5085243621","display_name":"Hengbin An","orcid":"https://orcid.org/0000-0001-8407-4119"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Heng-Bin An","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085243621"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2774,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.79057592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"5","first_page":"1850","last_page":"1871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9986000061035156,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.8156076669692993},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6915528774261475},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6456655263900757},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6358040571212769},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6278817057609558},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5976466536521912},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5793516039848328},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5211629867553711},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5131877064704895},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.5026075839996338},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3279534578323364},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24163717031478882},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.12776052951812744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11045828461647034},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.06541210412979126},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.046443551778793335}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8156076669692993},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6915528774261475},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6456655263900757},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6358040571212769},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6278817057609558},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5976466536521912},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5793516039848328},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5211629867553711},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5131877064704895},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.5026075839996338},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3279534578323364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24163717031478882},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.12776052951812744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11045828461647034},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.06541210412979126},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.046443551778793335},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040611653","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611653","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1826232933","https://openalex.org/W1975113089","https://openalex.org/W1978562552","https://openalex.org/W2009121431","https://openalex.org/W2010775269","https://openalex.org/W2024972953","https://openalex.org/W2045633650","https://openalex.org/W2048369486","https://openalex.org/W2053116529","https://openalex.org/W2068484625","https://openalex.org/W2074809615","https://openalex.org/W2079440004","https://openalex.org/W2090963365","https://openalex.org/W2092519144","https://openalex.org/W2107501462","https://openalex.org/W2130756427","https://openalex.org/W2140153041","https://openalex.org/W2160555573","https://openalex.org/W2171303908","https://openalex.org/W2509362106"],"related_works":["https://openalex.org/W1969458127","https://openalex.org/W2135034717","https://openalex.org/W2032940239","https://openalex.org/W2062707001","https://openalex.org/W2169562629","https://openalex.org/W2083136680","https://openalex.org/W4231955419","https://openalex.org/W2036958153","https://openalex.org/W2979236878","https://openalex.org/W2395990617"],"abstract_inverted_index":{"The":[0],"additive":[1],"Schwarz":[2],"preconditioned":[3],"inexact":[4,104],"Newton":[5,105],"(ASPIN)":[6],"method":[7,39,70,80,91],"was":[8,59],"recently":[9],"introduced":[10],"[X.-C.":[11],"Cai":[12],"and":[13,73,94],"D.":[14],"E.\\":[15],"Keyes,":[16],"{\\it":[17],"SIAM":[18],"J.":[19],"Sci.\\":[20],"Comput.},":[21],"24":[22],"(2002),":[23],"pp.":[24],"183--200]":[25],"to":[26,44,100],"solve":[27,45],"the":[28,37,64,68,74,85,89,95,103],"systems":[29],"of":[30,67,102],"nonlinear":[31,48],"equations":[32],"with":[33],"nonbalanced":[34],"nonlinearities.":[35],"Although":[36],"ASPIN":[38,69,90],"has":[40,53],"successfully":[41],"been":[42,55],"used":[43],"some":[46],"difficult":[47],"equations,":[49],"its":[50],"convergence":[51,65,86],"property":[52,66],"not":[54],"studied":[56],"since":[57],"it":[58],"proposed.":[60],"In":[61],"this":[62,79],"paper,":[63],"is":[71,81,92,98],"studied,":[72],"obtained":[75,96],"result":[76,97],"shows":[77],"that":[78,101],"locally":[82],"convergent.":[83],"Furthermore,":[84],"rate":[87],"for":[88],"discussed":[93],"similar":[99],"method.":[106]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
