{"id":"https://openalex.org/W2128181323","doi":"https://doi.org/10.1080/00207169908804843","title":"Further results on regular splittings and their applications to some iterative methods","display_name":"Further results on regular splittings and their applications to some iterative methods","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2128181323","doi":"https://doi.org/10.1080/00207169908804843","mag":"2128181323"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804843","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804843","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":null,"display_name":"Wang Xinmin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210154711","display_name":"Institute of Finance and Banking","ror":"https://ror.org/05qs80z63","country_code":"CN","type":"facility","lineage":["https://openalex.org/I114218197","https://openalex.org/I4210154711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wang Xinmin","raw_affiliation_strings":["\n                   \n               Department of Economic Information, 82 Management, Finance and Banking Institute of China, Beijing, 100 029, People's Republic of China","Department of Economic Information, 82 Management , Finance and Banking Institute of China , Beijing, 100 029, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Department of Economic Information, 82 Management, Finance and Banking Institute of China, Beijing, 100 029, People's Republic of China","institution_ids":["https://openalex.org/I4210154711"]},{"raw_affiliation_string":"Department of Economic Information, 82 Management , Finance and Banking Institute of China , Beijing, 100 029, People's Republic of China","institution_ids":["https://openalex.org/I4210154711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065466750","display_name":"M. Madalena Martins","orcid":"https://orcid.org/0000-0003-1694-5204"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"M. Madalena Martins","raw_affiliation_strings":["\n                   \n               Department of Mathematics, University of Coimbra, Coimbra, 3000, Portugal","Department of Mathematics , University of Coimbra , Coimbra, 3000, Portugal"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Department of Mathematics, University of Coimbra, Coimbra, 3000, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Department of Mathematics , University of Coimbra , Coimbra, 3000, Portugal","institution_ids":["https://openalex.org/I76903346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210154711"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22927077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"2","first_page":"167","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9936000108718872,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9905999898910522,"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":0.8318579196929932},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.8063350319862366},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.7557542324066162},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5790638327598572},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.5599337816238403},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5496387481689453},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4789750576019287},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40972304344177246},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34458452463150024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27571019530296326},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15958696603775024}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8318579196929932},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.8063350319862366},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.7557542324066162},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5790638327598572},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.5599337816238403},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5496387481689453},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4789750576019287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40972304344177246},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34458452463150024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27571019530296326},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15958696603775024},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804843","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804843","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1989435628","https://openalex.org/W2050170536","https://openalex.org/W2167055243","https://openalex.org/W2569133694","https://openalex.org/W2588081979","https://openalex.org/W3035235874"],"related_works":["https://openalex.org/W2372456425","https://openalex.org/W2374637297","https://openalex.org/W2011003221","https://openalex.org/W2360606995","https://openalex.org/W2281025351","https://openalex.org/W2373918471","https://openalex.org/W2356248141","https://openalex.org/W2348990883","https://openalex.org/W2392837218","https://openalex.org/W2134280096"],"abstract_inverted_index":{"In":[0,62],"this":[1],"paper":[2],"we":[3,47,65,101],"present":[4],"a":[5,41],"general":[6],"theorem":[7],"which":[8,146],"allows":[9],"the":[10,13,17,30,51,57,71,74,94,103,127,134,141,150],"comparison":[11],"of":[12,16,20,29,33,73,105],"spectral":[14],"radius":[15],"iteration":[18],"matrices":[19],"some":[21,125],"iterative":[22,59],"methods,":[23],"obtained":[24,152],"from":[25],"different":[26],"regular":[27],"splittings":[28],"matrix":[31],"A":[32,39],"Ax":[34],"=":[35],"b.":[36],"Thus,":[37,84],"when":[38,100],"is":[40,54,97,143],"non-singular":[42],"M-matrix,":[43],"not":[44],"necessary":[45],"irreducible,":[46],"can":[48,66,130],"prove":[49,122],"that":[50],"Gauss\u2013Seidel":[52],"method":[53,60,78,96,129,136],"faster":[55,82,98,132],"than":[56,99,133],"(SOR)":[58],"().":[61],"these":[63],"conditions,":[64],"choose":[67],"convenient":[68],"values":[69],"for":[70],"parameters":[72],"Generalised":[75],"Accelerated":[76],"Overrelaxation":[77],"(GAOR)":[79,95],"and":[80,116,117,148],"get":[81],"results.":[83],"with":[85,107,118],"0":[86,108],"<":[87,109],"r":[88,110],"2,":[89],"w":[90,112],"2":[91],"\u2264":[92,114],"1":[93,111,113,115],"approximate":[102],"solution":[104],"Ax=b":[106],".":[119],"We":[120],"also":[121,144],"that,":[123],"under":[124,138],"assumptions,":[126,140],"GAOR":[128],"be":[131],"AOR":[135],"and,":[137],"other":[139],"reverse":[142],"true":[145],"improves":[147],"generalises":[149],"results":[151],"in":[153],"[3].":[154]},"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
