{"id":"https://openalex.org/W2050154031","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","title":"OnM-multisplittings of singularM-matrices with application to Markov chains","display_name":"OnM-multisplittings of singularM-matrices with application to Markov chains","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2050154031","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","mag":"2050154031"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5085341518","display_name":"Rafael Bru","orcid":"https://orcid.org/0000-0003-1123-5617"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Rafael Bru","raw_affiliation_strings":["Departament de Matema\u0300tica Aplicada, Universitat Polite\u0300cnica de Vale\u0300ncia, E-46071 Vale\u0300ncia, Spain","Departament de Matem\u00e0tica Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E\u201046071 Val\u00e8ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matema\u0300tica Aplicada, Universitat Polite\u0300cnica de Vale\u0300ncia, E-46071 Vale\u0300ncia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E\u201046071 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062095521","display_name":"Rafael Cant\u00f3","orcid":"https://orcid.org/0000-0002-1341-2800"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Cant\u00f3","raw_affiliation_strings":["Departament de Matema\u0300tica Aplicada, Universitat Polite\u0300cnica de Vale\u0300ncia, E-46071 Vale\u0300ncia, Spain","Departament de Matem\u00e0tica Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E\u201046071 Val\u00e8ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matema\u0300tica Aplicada, Universitat Polite\u0300cnica de Vale\u0300ncia, E-46071 Vale\u0300ncia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E\u201046071 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001449750","display_name":"Joan\u2010Josep Climent","orcid":"https://orcid.org/0000-0003-0522-0304"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]},{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["ES","US"],"is_corresponding":false,"raw_author_name":"Joan-Josep Climent","raw_affiliation_strings":["Departament de Cie\u0300ncia de la Computacio\u0301 i Intel\u00b7lige\u0300ncia Artificial, Universitat d'Alacant, E-03071 Alacant, Spain","Departament de Ci\u00e8ncia de la Computaci\u00f3 i Intel\u00b7lig\u00e8ncia Artificial, Universitat d'Alacant, E\u201003071 Alacant, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Cie\u0300ncia de la Computacio\u0301 i Intel\u00b7lige\u0300ncia Artificial, Universitat d'Alacant, E-03071 Alacant, Spain","institution_ids":["https://openalex.org/I130194489"]},{"raw_affiliation_string":"Departament de Ci\u00e8ncia de la Computaci\u00f3 i Intel\u00b7lig\u00e8ncia Artificial, Universitat d'Alacant, E\u201003071 Alacant, Spain","institution_ids":["https://openalex.org/I1343180700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085341518"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":1.4725,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82001837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"5","issue":"4","first_page":"299","last_page":"311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13685","display_name":"Material Science and Thermodynamics","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7864245772361755},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.732977032661438},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.6111308932304382},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5600874423980713},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4737095236778259},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41665107011795044},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4166051745414734},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.4136779308319092},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3005945682525635},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2998230457305908},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2603362202644348}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7864245772361755},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.732977032661438},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.6111308932304382},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5600874423980713},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4737095236778259},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41665107011795044},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4166051745414734},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.4136779308319092},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3005945682525635},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2998230457305908},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2603362202644348},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<299::aid-nla103>3.0.co;2-v","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","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":16,"referenced_works":["https://openalex.org/W1964818805","https://openalex.org/W1970261865","https://openalex.org/W1980500205","https://openalex.org/W1985921170","https://openalex.org/W1996958562","https://openalex.org/W2023455365","https://openalex.org/W2026304610","https://openalex.org/W2050488651","https://openalex.org/W2053194152","https://openalex.org/W2083883802","https://openalex.org/W2085207070","https://openalex.org/W2569133694","https://openalex.org/W3035235874","https://openalex.org/W4253667705","https://openalex.org/W4295016751","https://openalex.org/W6779857112"],"related_works":["https://openalex.org/W2350399343","https://openalex.org/W2383395740","https://openalex.org/W2134280096","https://openalex.org/W2189112453","https://openalex.org/W2389850603","https://openalex.org/W4234931342","https://openalex.org/W4241673800","https://openalex.org/W1990099360","https://openalex.org/W2031472999","https://openalex.org/W2138831083"],"abstract_inverted_index":{"Given":[0],"a":[1,5,43,104],"singular":[2,50],"M\u2013matrix":[3],"of":[4,20,25,39,81,98,115,119],"linear":[6,51],"system,":[7],"convergent":[8],"conditions":[9],"under":[10,68],"which":[11,55],"iterative":[12],"schemes":[13],"based":[14,85],"on":[15,86],"M\u2013multisplittings":[16],"are":[17,33],"studied.":[18],"Two":[19],"those":[21,38],"conditions,":[22,71],"the":[23,26,40,72,94,113,120],"index":[24],"iteration":[27,46],"matrix":[28,118],"and":[29,35,65,75],"its":[30],"spectral":[31],"radius":[32],"investigated":[34],"related":[36],"to":[37,59],"M-matrix.":[41],"Furthermore,":[42],"parallel":[44],"multisplitting":[45,83,121],"scheme":[47],"for":[48,92],"solving":[49],"systems":[52],"is":[53,90,122],"suggested":[54],"can":[56,108],"be":[57,109],"applied":[58],"practical":[60],"problems":[61,67],"such":[62],"as":[63],"Poisson":[64],"elasticity":[66],"certain":[69],"boundary":[70],"Neumann":[73],"problem,":[74],"in":[76],"Markov":[77,99],"chains.":[78,100],"A":[79],"discussion":[80],"that":[82],"scheme,":[84],"Gauss\u2013Seidel":[87],"type":[88],"splittings":[89],"given":[91],"computing":[93],"stationary":[95],"distribution":[96],"vector":[97],"In":[101],"this":[102],"case":[103],"computational":[105],"viable":[106],"algorithm":[107],"constructed,":[110],"since":[111],"only":[112],"nonsingularity":[114],"one":[116],"weighting":[117],"needed.":[123],"\u00a9":[124],"1998":[125],"John":[126],"Wiley":[127],"&":[128],"Sons,":[129],"Ltd.":[130]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
