{"id":"https://openalex.org/W2162277654","doi":"https://doi.org/10.1080/00207160213943","title":"Note To The Mixed-Type Splitting Iterative Method For The Positive Real Linear System","display_name":"Note To The Mixed-Type Splitting Iterative Method For The Positive Real Linear System","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2162277654","doi":"https://doi.org/10.1080/00207160213943","mag":"2162277654"},"language":"en","primary_location":{"id":"doi:10.1080/00207160213943","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160213943","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/A5101876245","display_name":"Changjun Li","orcid":"https://orcid.org/0000-0003-1272-3487"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I142078773","display_name":"Shenyang Institute of Automation","ror":"https://ror.org/00ft6nj33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Changjun Li","raw_affiliation_strings":["a   Shenyang Institute of Automation , Chinese Academy of Sciences ,  China","Shenyang Institute of Automation , Chinese Academy of Sciences , China"],"affiliations":[{"raw_affiliation_string":"a   Shenyang Institute of Automation , Chinese Academy of Sciences ,  China","institution_ids":["https://openalex.org/I142078773"]},{"raw_affiliation_string":"Shenyang Institute of Automation , Chinese Academy of Sciences , China","institution_ids":["https://openalex.org/I142078773","https://openalex.org/I19820366"]}]},{"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/I52590639","display_name":"Nottingham Trent University","ror":"https://ror.org/04xyxjd90","country_code":"GB","type":"education","lineage":["https://openalex.org/I52590639"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David Evans","raw_affiliation_strings":["b  Nottingham Trent University ,  Nottingham ,  UK","Nottingham Trent University , Nottingham , UK"],"affiliations":[{"raw_affiliation_string":"b  Nottingham Trent University ,  Nottingham ,  UK","institution_ids":["https://openalex.org/I52590639"]},{"raw_affiliation_string":"Nottingham Trent University , Nottingham , UK","institution_ids":["https://openalex.org/I52590639"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101876245"],"corresponding_institution_ids":["https://openalex.org/I142078773","https://openalex.org/I19820366"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.23258771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"79","issue":"11","first_page":"1201","last_page":"1209"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9915000200271606,"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":0.9908000230789185,"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":0.7876690626144409},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.7778580188751221},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.6612968444824219},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6116445660591125},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5916911959648132},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4962993264198303},{"id":"https://openalex.org/keywords/convergent-matrix","display_name":"Convergent matrix","score":0.45507892966270447},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45082661509513855},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4498459994792938},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.424429714679718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40287357568740845},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3055573105812073},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.18273606896400452},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.14566341042518616},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09605619311332703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06292134523391724}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7876690626144409},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.7778580188751221},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.6612968444824219},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6116445660591125},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5916911959648132},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4962993264198303},{"id":"https://openalex.org/C9848182","wikidata":"https://www.wikidata.org/wiki/Q5166397","display_name":"Convergent matrix","level":5,"score":0.45507892966270447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45082661509513855},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4498459994792938},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.424429714679718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40287357568740845},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3055573105812073},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.18273606896400452},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.14566341042518616},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09605619311332703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06292134523391724},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160213943","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160213943","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"},{"id":"pmh:oai:irep.ntu.ac.uk:12176","is_oa":false,"landing_page_url":"http://irep.ntu.ac.uk/id/eprint/12176/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400559","display_name":"Nottingham Trent University's Institutional Repository (Nottingham Trent Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I52590639","host_organization_name":"Nottingham Trent University","host_organization_lineage":["https://openalex.org/I52590639"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W121573721","https://openalex.org/W1969290389","https://openalex.org/W2004970748","https://openalex.org/W2029431083","https://openalex.org/W2065680376","https://openalex.org/W2132476090","https://openalex.org/W2588081979","https://openalex.org/W2781884436","https://openalex.org/W3035235874","https://openalex.org/W4299343067"],"related_works":["https://openalex.org/W2366222664","https://openalex.org/W2352030154","https://openalex.org/W27112594","https://openalex.org/W1664553927","https://openalex.org/W2161209494","https://openalex.org/W2353317030","https://openalex.org/W2374901252","https://openalex.org/W2162277654","https://openalex.org/W1977669169","https://openalex.org/W2360955067"],"abstract_inverted_index":{"In":[0,74],"[5]":[1],"a":[2,45],"new":[3,39,99,117],"iterative":[4,40,58,61,100,118],"method":[5,41,62,101,119,137],"is":[6,18,26,35,42,53,69,80,88,102,106,131,144],"given":[7],"for":[8],"the":[9,49,55,77,98,116,121,134,140,147,151],"linear":[10],"system":[11,143],"of":[12,48,94,113,150],"equations":[13],"Au=b":[14],",":[15,97,115],"where":[16],"A":[17,34,51],"large,":[19],"sparse":[20],"and":[21,23,28,52,86,155],"nonsymmetrical":[22],"A^{\\rm":[24],"T}+A":[25],"symmetric":[27],"positive":[29,36,141],"definite":[30],"(SPD)":[31],"or":[32],"equivalently":[33],"real.":[37],"The":[38,60],"based":[43],"on":[44],"mixed-type":[46,56],"splitting":[47,57],"matrix":[50,66,79],"called":[54],"method.":[59,128],"contains":[63],"an":[64],"auxiliary":[65,78],"D_1":[67],"that":[68,90,109,133],"restricted":[70],"to":[71,82,139],"be":[72,83],"symmetric.":[73],"this":[75],"note,":[76],"allowed":[81],"more":[84],"general":[85],"it":[87,130],"shown":[89,108,132],"by":[91,110],"proper":[92,148],"choice":[93,112,149],"D":[95],"1":[96],"still":[103],"convergent.":[104],"It":[105],"also":[107],"special":[111],"D_{1}":[114],"becomes":[120],"well-known":[122],"(point)":[123,135],"accelerated":[124],"overrelaxation":[125,152],"(AOR)":[126],"[1]":[127],"Hence,":[129],"AOR":[136],"applied":[138],"real":[142],"convergent":[145],"under":[146],"parameters":[153],"y":[154],".":[156]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}