{"id":"https://openalex.org/W2114065885","doi":"https://doi.org/10.1080/00207169708804614","title":"The multisplitting PSD (MPSD) method for systems of weakly nonlinear equations","display_name":"The multisplitting PSD (MPSD) method for systems of weakly nonlinear equations","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2114065885","doi":"https://doi.org/10.1080/00207169708804614","mag":"2114065885"},"language":"en","primary_location":{"id":"doi:10.1080/00207169708804614","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804614","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5050773996","display_name":"Da\u2010Wei Chang","orcid":"https://orcid.org/0000-0002-4317-7979"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Da-Wei Chang","raw_affiliation_strings":["Department of Mathematics of Shaanxi , Normal University , Xi'an, 710062, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics of Shaanxi , Normal University , Xi'an, 710062, P.R. China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050773996"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":1.0048,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77605258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"65","issue":"3-4","first_page":"247","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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":0.9987000226974487,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.998199999332428,"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":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8597760200500488},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6945076584815979},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5602011680603027},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4905363917350769},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42058265209198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8597760200500488},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6945076584815979},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5602011680603027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4905363917350769},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42058265209198},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169708804614","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804614","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1582788465","https://openalex.org/W1970261865","https://openalex.org/W1975563825","https://openalex.org/W1990772930","https://openalex.org/W2000212348","https://openalex.org/W2004432435","https://openalex.org/W2036614499","https://openalex.org/W2038486641","https://openalex.org/W2054791853","https://openalex.org/W2083883802","https://openalex.org/W2090963365","https://openalex.org/W2093993556","https://openalex.org/W2478091498","https://openalex.org/W2588081979","https://openalex.org/W3035235874","https://openalex.org/W4295016751","https://openalex.org/W4299343067","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W1506216622","https://openalex.org/W1987033902","https://openalex.org/W2207380610","https://openalex.org/W2362641799","https://openalex.org/W2038137143","https://openalex.org/W3213335643","https://openalex.org/W2141137682","https://openalex.org/W4292604635","https://openalex.org/W2098406473","https://openalex.org/W2769625221"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"the":[5,28,34,38],"parallel":[6],"multisplitting":[7],"PSD":[8],"(MPSD)":[9],"method":[10],"for":[11],"solving":[12],"system":[13],"of":[14,27],"weakly":[15],"nonlinear":[16],"equations":[17],"Ax":[18],"+":[19],"\u0444(x)":[20],"=":[21],"b.":[22],"The":[23],"global":[24],"convergence":[25],"theorem":[26],"MPSD":[29],"algorithm":[30,48],"is":[31,49],"established":[32],"under":[33],"some":[35],"conditions.":[36],"Finally,":[37],"numerical":[39],"examples":[40],"are":[41],"given,":[42],"they":[43],"show":[44],"that":[45],"our":[46],"new":[47],"feasible":[50],"and":[51],"efficient.":[52]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}