{"id":"https://openalex.org/W2009462445","doi":"https://doi.org/10.1080/10637199508915518","title":"MULTISPLITTING RELAXED METHODS FOR A CLASS OF SYSTEM OF NONLINEAR EQUATIONS","display_name":"MULTISPLITTING RELAXED METHODS FOR A CLASS OF SYSTEM OF NONLINEAR EQUATIONS","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2009462445","doi":"https://doi.org/10.1080/10637199508915518","mag":"2009462445"},"language":"en","primary_location":{"id":"doi:10.1080/10637199508915518","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199508915518","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","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/A5108103543","display_name":"Wang Deren","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"WANG DEREN","raw_affiliation_strings":["Department of Mathematics , Shanghai University of Science and Technology , Shanghai, 201800, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shanghai University of Science and Technology , Shanghai, 201800, P.R. China","institution_ids":["https://openalex.org/I148128674","https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103371129","display_name":"Bai Zhongzhi","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BAI ZHONGZHI","raw_affiliation_strings":["Institute of Mathematics , Fudan University , Shanghai, 200433, P.R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Fudan University , Shanghai, 200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058624133","display_name":"David J. Evans","orcid":"https://orcid.org/0000-0001-6009-0333"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. J. EVANS","raw_affiliation_strings":["Parallel Algorithms Research Center , Loughborough University of Technology , Loughborough, Leicestershire, LE11 3TU, UK"],"affiliations":[{"raw_affiliation_string":"Parallel Algorithms Research Center , Loughborough University of Technology , Loughborough, Leicestershire, LE11 3TU, UK","institution_ids":["https://openalex.org/I143804889"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108103543"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I148128674"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16756757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"1-2","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9994000196456909,"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":0.9969000220298767,"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/uniqueness","display_name":"Uniqueness","score":0.7764725089073181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7380081415176392},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7108386754989624},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.592439591884613},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5836203098297119},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5658515095710754},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5023798942565918},{"id":"https://openalex.org/keywords/simultaneous-equations","display_name":"Simultaneous equations","score":0.4845382571220398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4689314663410187},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.46629446744918823},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4660217761993408},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44960692524909973},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4194907248020172},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14031100273132324},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08961722254753113},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07996180653572083}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7764725089073181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7380081415176392},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7108386754989624},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.592439591884613},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5836203098297119},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5658515095710754},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5023798942565918},{"id":"https://openalex.org/C170036204","wikidata":"https://www.wikidata.org/wiki/Q735660","display_name":"Simultaneous equations","level":3,"score":0.4845382571220398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4689314663410187},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.46629446744918823},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4660217761993408},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44960692524909973},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4194907248020172},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14031100273132324},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08961722254753113},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07996180653572083},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10637199508915518","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199508915518","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1969290389","https://openalex.org/W1970261865","https://openalex.org/W1975563825","https://openalex.org/W1976276100","https://openalex.org/W2011094287","https://openalex.org/W2083883802","https://openalex.org/W2090963365","https://openalex.org/W2093993556","https://openalex.org/W2321653420","https://openalex.org/W3035235874","https://openalex.org/W4297926604"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W315993174"],"abstract_inverted_index":{"We":[0],"set":[1],"up":[2],"a":[3,38],"class":[4],"of":[5,13,48,63,66,69],"parallel":[6],"multisplilting":[7],"relaxed":[8],"methods":[9],"for":[10,77],"the":[11,46,59,64,73,78],"system":[12,68],"nonlinear":[14],"equations":[15],"A\u03d5(u)":[16],"+":[17],"T\u03c8(u)":[18],"=":[19],"G":[20,32],"(u)":[21],"with":[22],"A,T\u03b5L(Rn":[23],"),\u03d5,\u03c8":[24],":Rn":[25],"\u2192":[26,35],"Rn":[27,34,36],"being":[28,37],"diagonal":[29],"mappings":[30],"and":[31,61,71],":":[33],"general":[39],"mapping,":[40],"which":[41],"is":[42],"generally":[43],"resulted":[44],"from":[45],"discretization":[47],"many":[49],"classical":[50],"differential":[51],"equations.":[52],"Under":[53],"rather":[54],"proper":[55],"conditions,":[56],"we":[57],"confirm":[58],"existence":[60],"uniqueness":[62],"solution":[65],"this":[67],"equations,":[70],"establish":[72],"global":[74],"convergence":[75],"theories":[76],"new":[79],"methods.":[80]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}