{"id":"https://openalex.org/W2125835361","doi":"https://doi.org/10.1137/140987936","title":"On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems","display_name":"On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2125835361","doi":"https://doi.org/10.1137/140987936","mag":"2125835361"},"language":"en","primary_location":{"id":"doi:10.1137/140987936","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140987936","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5113970855","display_name":"Zhong\u2010Zhi Bai","orcid":null},"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/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhong-Zhi Bai","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047172374","display_name":"Miroslav Rozlo\u017e\u0144\u0131k","orcid":"https://orcid.org/0000-0002-4328-9970"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miroslav Rozlo\u017en\u00cdk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113970855"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"],"apc_list":null,"apc_paid":null,"fwci":2.9083,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.91373195,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"53","issue":"4","first_page":"1716","last_page":"1737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9973000288009644,"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":0.9957000017166138,"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":0.8220332264900208},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6074427962303162},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.566419780254364},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.5519239902496338},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.546042263507843},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5402611494064331},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28069302439689636},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.21341031789779663},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.20803120732307434},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08065038919448853}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8220332264900208},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6074427962303162},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.566419780254364},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.5519239902496338},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.546042263507843},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5402611494064331},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28069302439689636},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.21341031789779663},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.20803120732307434},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08065038919448853},{"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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140987936","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140987936","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:asep.lib.cas.cz:CavUnEpca/0444138","is_oa":false,"landing_page_url":"http://hdl.handle.net/11104/0246711","pdf_url":null,"source":{"id":"https://openalex.org/S7407055266","display_name":"ASEP","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W224455513","https://openalex.org/W656642513","https://openalex.org/W1496738390","https://openalex.org/W1500709119","https://openalex.org/W1590879322","https://openalex.org/W1963924275","https://openalex.org/W1970210326","https://openalex.org/W1979360367","https://openalex.org/W1982804731","https://openalex.org/W1984091866","https://openalex.org/W1984840642","https://openalex.org/W1985931672","https://openalex.org/W1987613138","https://openalex.org/W2002102128","https://openalex.org/W2003372231","https://openalex.org/W2020804487","https://openalex.org/W2030692319","https://openalex.org/W2034236710","https://openalex.org/W2041843456","https://openalex.org/W2049157754","https://openalex.org/W2088456940","https://openalex.org/W2095036901","https://openalex.org/W2108291106","https://openalex.org/W2119862562","https://openalex.org/W2148071792","https://openalex.org/W2164050538","https://openalex.org/W2798909945","https://openalex.org/W3005231780","https://openalex.org/W3035235874"],"related_works":["https://openalex.org/W4285308861","https://openalex.org/W2011634686","https://openalex.org/W200996852","https://openalex.org/W2356831339","https://openalex.org/W1972612702","https://openalex.org/W3113626245","https://openalex.org/W2360264057","https://openalex.org/W2797540493","https://openalex.org/W4251679243","https://openalex.org/W1979435176"],"abstract_inverted_index":{"We":[0,22,78],"study":[1],"the":[2,33,39,42,66,99],"numerical":[3,112],"behavior":[4],"of":[5,19,27,41,83,92],"stationary":[6,53],"one-step":[7,117],"or":[8,72,75],"two-step":[9,121],"matrix":[10,34,54,84],"splitting":[11,55,85,122],"iteration":[12,56,86,123],"methods":[13,87],"for":[14],"solving":[15],"large":[16],"sparse":[17],"systems":[18,30],"linear":[20,29],"equations.":[21],"show":[23],"that":[24,90],"inexact":[25,103,116,120],"solutions":[26,44],"inner":[28,104],"associated":[31],"with":[32,114],"splittings":[35],"may":[36],"considerably":[37],"influence":[38],"accuracy":[40],"approximate":[43],"computed":[45],"in":[46],"finite":[47],"precision":[48],"arithmetic.":[49],"For":[50],"a":[51],"general":[52],"method,":[57],"we":[58],"analyze":[59],"two":[60,80],"mathematically":[61],"equivalent":[62],"implementations":[63],"and":[64,88,118],"discuss":[65],"conditions":[67],"when":[68,101],"they":[69],"are":[70,109],"componentwise":[71],"normwise":[73],"forward":[74],"backward":[76],"stable.":[77],"distinguish":[79],"different":[81],"forms":[82],"prove":[89],"one":[91],"them":[93],"is":[94],"significantly":[95],"more":[96],"accurate":[97],"than":[98],"other":[100],"employing":[102],"solves.":[105],"The":[106],"theoretical":[107],"results":[108],"illustrated":[110],"by":[111],"experiments":[113],"an":[115,119],"method.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-08T08:50:53.379069","created_date":"2025-10-10T00:00:00"}