{"id":"https://openalex.org/W2125231399","doi":"https://doi.org/10.1137/040616541","title":"Additive Schwarz Iterations for Markov Chains","display_name":"Additive Schwarz Iterations for Markov Chains","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2125231399","doi":"https://doi.org/10.1137/040616541","mag":"2125231399"},"language":"en","primary_location":{"id":"doi:10.1137/040616541","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040616541","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis 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/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":["Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038882796","display_name":"Francisco Pedroche","orcid":"https://orcid.org/0000-0001-6521-4331"},"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":"Francisco Pedroche","raw_affiliation_strings":["Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047875137","display_name":"Daniel B. Szyld","orcid":"https://orcid.org/0000-0001-8010-0391"},"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":"Daniel B. Szyld","raw_affiliation_strings":["Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Institut de Matem\u00e0tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s/n. 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085341518"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":null,"apc_paid":null,"fwci":3.3672,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.9281394,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"445","last_page":"458"},"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":0.9983999729156494,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8548374176025391},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6454219818115234},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5356841087341309},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.5122910737991333},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.49968528747558594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49455901980400085},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4375850260257721},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4273393154144287},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3007791042327881},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.2403157353401184},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17542630434036255},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.12174305319786072}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8548374176025391},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6454219818115234},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5356841087341309},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.5122910737991333},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.49968528747558594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49455901980400085},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4375850260257721},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4273393154144287},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3007791042327881},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.2403157353401184},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17542630434036255},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.12174305319786072},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040616541","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040616541","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.8529","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.8529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.temple.edu/~szyld/papers/simax61654.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3115803529","display_name":"Flexible Krylov Methods and Schwarz Preconditioners","funder_award_id":"0207525","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320312387","display_name":"Temple University","ror":"https://ror.org/00kx1jb78"},{"id":"https://openalex.org/F4320321864","display_name":"Generalitat Valenciana","ror":"https://ror.org/0097mvx21"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1500566338","https://openalex.org/W1500921805","https://openalex.org/W1514324734","https://openalex.org/W1542243431","https://openalex.org/W1548589512","https://openalex.org/W1969139579","https://openalex.org/W1978286021","https://openalex.org/W1980500205","https://openalex.org/W2000582360","https://openalex.org/W2005124301","https://openalex.org/W2008808718","https://openalex.org/W2027158013","https://openalex.org/W2050653429","https://openalex.org/W2063333912","https://openalex.org/W2088276185","https://openalex.org/W2095749831","https://openalex.org/W2106990738","https://openalex.org/W2109044896","https://openalex.org/W2117625969","https://openalex.org/W2119862562","https://openalex.org/W2159099413","https://openalex.org/W2569133694","https://openalex.org/W3035235874"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W2028890215","https://openalex.org/W2159100661","https://openalex.org/W2000290814","https://openalex.org/W3839471","https://openalex.org/W2339825459","https://openalex.org/W2138840323","https://openalex.org/W1994696552","https://openalex.org/W1515964003","https://openalex.org/W2367747968"],"abstract_inverted_index":{"A":[0],"convergence":[1,89,99],"analysis":[2],"is":[3,34,76,84],"presented":[4],"for":[5,121],"additive":[6,138],"Schwarz":[7,53,139,156],"iterations":[8],"when":[9],"applied":[10],"to":[11,26,38,45,86,112],"consistent":[12],"singular":[13,27,129],"systems":[14,39],"of":[15,17,48,60,66,82,90,106,116,124],"equations":[16],"the":[18,64,69,78,88,91,94,107,114,122],"form":[19],"Ax":[20],"=":[21],"b.":[22],"The":[23,80],"theory":[24],"applies":[25],"M-matrices":[28],"with":[29,151],"one-dimensional":[30],"null":[31],"space":[32],"and":[33,44,127,154],"applicable":[35],"in":[36,93],"particular":[37],"representing":[40],"ergodic":[41],"Markov":[42,125],"chains,":[43],"certain":[46],"discretizations":[47],"partial":[49],"differential":[50],"equations.":[51],"Additive":[52],"can":[54],"be":[55],"seen":[56],"as":[57,101,103],"a":[58,147],"generalization":[59],"block":[61,143,152],"Jacobi,":[62],"where":[63],"set":[65],"indices":[67],"defining":[68],"diagonal":[70],"blocks":[71],"have":[72],"nonempty":[73],"intersection;":[74],"this":[75,117],"called":[77],"overlap.":[79],"presence":[81],"overlap":[83],"known":[85],"accelerate":[87],"methods":[92],"nonsingular":[95],"case.":[96],"By":[97],"providing":[98],"results,":[100],"well":[102],"some":[104],"characteristics":[105],"induced":[108],"splitting,":[109],"we":[110],"hope":[111],"encourage":[113],"use":[115],"additional":[118],"computational":[119],"tool":[120],"solution":[123],"chains":[126],"other":[128],"systems.":[130],"We":[131],"present":[132],"several":[133],"numerical":[134,149],"examples":[135],"showing":[136],"that":[137],"performs":[140],"better":[141],"than":[142],"Jacobi.":[144],"For":[145],"completeness,":[146],"few":[148],"experiments":[150],"Gauss\u2013Seidel":[153],"multiplicative":[155],"are":[157],"also":[158],"included.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
