{"id":"https://openalex.org/W2050431046","doi":"https://doi.org/10.1137/s106482759631370x","title":"Multiparameter Iterative Schemes for the Solution of Systems of Linear and Nonlinear Equations","display_name":"Multiparameter Iterative Schemes for the Solution of Systems of Linear and Nonlinear Equations","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2050431046","doi":"https://doi.org/10.1137/s106482759631370x","mag":"2050431046"},"language":"en","primary_location":{"id":"doi:10.1137/s106482759631370x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759631370x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5022162225","display_name":"Claude Brezinski","orcid":"https://orcid.org/0000-0002-2209-4306"},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"C. Brezinski","raw_affiliation_strings":["Lille University of Science and Technology#TAB#"],"affiliations":[{"raw_affiliation_string":"Lille University of Science and Technology#TAB#","institution_ids":["https://openalex.org/I2279609970"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034765003","display_name":"Jean\u2010Paul Chehab","orcid":"https://orcid.org/0000-0003-2193-6863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. P. Chehab","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022162225"],"corresponding_institution_ids":["https://openalex.org/I2279609970"],"apc_list":null,"apc_paid":null,"fwci":1.4652,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.81927507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"6","first_page":"2140","last_page":"2159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.8421294093132019},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6691826581954956},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6309789419174194},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6240418553352356},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6228232383728027},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5696889758110046},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5475559830665588},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49160701036453247},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4893280863761902},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4873693585395813},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4590193033218384},{"id":"https://openalex.org/keywords/successive-over-relaxation","display_name":"Successive over-relaxation","score":0.4243814945220947},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.38625600934028625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27531561255455017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.205440491437912}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8421294093132019},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6691826581954956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6309789419174194},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6240418553352356},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6228232383728027},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5696889758110046},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5475559830665588},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49160701036453247},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4893280863761902},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4873693585395813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4590193033218384},{"id":"https://openalex.org/C127042158","wikidata":"https://www.wikidata.org/wiki/Q1561270","display_name":"Successive over-relaxation","level":4,"score":0.4243814945220947},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.38625600934028625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27531561255455017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.205440491437912},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s106482759631370x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759631370x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.526.9154","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.526.9154","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathinfo.u-picardie.fr/chehab/Rech/brezinskichehabsiam.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W108141292","https://openalex.org/W164251211","https://openalex.org/W569324415","https://openalex.org/W622907106","https://openalex.org/W1564995869","https://openalex.org/W1594759473","https://openalex.org/W1965193952","https://openalex.org/W1978429153","https://openalex.org/W1979026536","https://openalex.org/W1980177911","https://openalex.org/W1983283283","https://openalex.org/W1988864263","https://openalex.org/W2004688581","https://openalex.org/W2018008274","https://openalex.org/W2023743841","https://openalex.org/W2034231638","https://openalex.org/W2062860872","https://openalex.org/W2063175726","https://openalex.org/W2071805662","https://openalex.org/W2155216327","https://openalex.org/W2163612185","https://openalex.org/W2276773316","https://openalex.org/W2520889055","https://openalex.org/W2523925953","https://openalex.org/W2539260985","https://openalex.org/W2606126658","https://openalex.org/W3147515309","https://openalex.org/W4249012403"],"related_works":["https://openalex.org/W2141137682","https://openalex.org/W3119667263","https://openalex.org/W2043360208","https://openalex.org/W2412311587","https://openalex.org/W2769625221","https://openalex.org/W2281025351","https://openalex.org/W2356777845","https://openalex.org/W2433204144","https://openalex.org/W2298576417","https://openalex.org/W3000131912"],"abstract_inverted_index":{"In":[0,82,136],"this":[1,86],"paper,":[2],"we":[3,88],"introduce":[4],"multiparameter":[5,90,141],"generalizations":[6],"of":[7,18,35,40,66,78,92,109,117,122],"the":[8,36,41,56,62,79,93,107,110,115,139,144,149],"linear":[9,19,119],"and":[10,20,121],"nonlinear":[11,21,99,124],"iterative":[12],"Richardson":[13],"methods":[14],"for":[15,97],"solving":[16,98],"systems":[17],"equations.":[22],"The":[23,45],"new":[24,111],"algorithms":[25],"are":[26],"based":[27],"on":[28],"using":[29],"a":[30,118,123,130],"(optimal)":[31,37,140,150],"matricial":[32],"relaxation":[33,39,142],"instead":[34],"scalar":[38,151],"steepest":[42],"descent":[43],"method.":[44],"optimal":[46],"matrix,":[47],"which":[48,126,133],"is":[49,59,72],"defined":[50],"at":[51],"each":[52],"iteration":[53],"by":[54],"minimizing":[55],"current":[57],"residual,":[58],"computed":[60],"as":[61,146],"least":[63],"squares":[64],"solution":[65,116],"an":[67],"associated":[68],"problem":[69,120,132],"whose":[70],"dimension":[71],"generally":[73],"much":[74],"lower":[75],"than":[76],"that":[77],"original":[80],"problem.":[81],"particular,":[83],"thanks":[84],"to":[85,148],"approach,":[87],"construct":[89],"versions":[91],"$\\Delta^k$":[94],"method":[95],"introduced":[96],"fixed":[100],"point":[101],"problems.":[102],"Various":[103],"numerical":[104],"results":[105],"illustrate":[106],"implementation":[108],"schemes.":[112],"They":[113],"concern":[114],"one":[125],"comes":[127],"out":[128],"from":[129],"reaction-diffusion":[131],"exhibits":[134],"bifurcations.":[135],"both":[137],"cases,":[138],"improves":[143],"convergence":[145],"compared":[147],"one.":[152]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
