{"id":"https://openalex.org/W2063646381","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","title":"Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices","display_name":"Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2063646381","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","mag":"2063646381"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","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/A5039515540","display_name":"Ivo Marek","orcid":"https://orcid.org/0000-0002-7063-4434"},"institutions":[{"id":"https://openalex.org/I35913352","display_name":"Prague University of Economics and Business","ror":"https://ror.org/029ecwj92","country_code":"CZ","type":"education","lineage":["https://openalex.org/I35913352"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Ivo Marek","raw_affiliation_strings":["Katedra Numericke\u0301 Matematicky, Na Matematicko \u2013 Fyzika\u0301lni\u0301 Fakulte\u0302, University Karlovy, Malostranske\u0301 na\u0301m. 25, 118 00 Praha 1, Czech Republic","Katedra Numerick\u00e9 Matematicky, Na Matematicko \u2013 Fyzik\u00e1ln\u00ed Fakult\u00ea, University Karlovy, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Katedra Numericke\u0301 Matematicky, Na Matematicko \u2013 Fyzika\u0301lni\u0301 Fakulte\u0302, University Karlovy, Malostranske\u0301 na\u0301m. 25, 118 00 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I35913352"]},{"raw_affiliation_string":"Katedra Numerick\u00e9 Matematicky, Na Matematicko \u2013 Fyzik\u00e1ln\u00ed Fakult\u00ea, University Karlovy, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I35913352"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072108003","display_name":"Petr Mayer","orcid":null},"institutions":[{"id":"https://openalex.org/I35913352","display_name":"Prague University of Economics and Business","ror":"https://ror.org/029ecwj92","country_code":"CZ","type":"education","lineage":["https://openalex.org/I35913352"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Petr Mayer","raw_affiliation_strings":["Katedra Numericke\u0301 Matematicky, Na Matematicko \u2013 Fyzika\u0301lni\u0301 Fakulte\u0302, University Karlovy, Malostranske\u0301 na\u0301m. 25, 118 00 Praha 1, Czech Republic","Katedra Numerick\u00e9 Matematicky, Na Matematicko \u2013 Fyzik\u00e1ln\u00ed Fakult\u00ea, University Karlovy, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Katedra Numericke\u0301 Matematicky, Na Matematicko \u2013 Fyzika\u0301lni\u0301 Fakulte\u0302, University Karlovy, Malostranske\u0301 na\u0301m. 25, 118 00 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I35913352"]},{"raw_affiliation_string":"Katedra Numerick\u00e9 Matematicky, Na Matematicko \u2013 Fyzik\u00e1ln\u00ed Fakult\u00ea, University Karlovy, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I35913352"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039515540","https://openalex.org/A5072108003"],"corresponding_institution_ids":["https://openalex.org/I35913352"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":1.9633,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.86235078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"4","first_page":"253","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9857000112533569,"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":0.9857000112533569,"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":0.9811000227928162,"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/convergence","display_name":"Convergence (economics)","score":0.7937495112419128},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7212710380554199},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.7137643098831177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6713021993637085},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.591865599155426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5584880709648132},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.4520570635795593},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4498519003391266},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.43056678771972656},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34082257747650146},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2315465211868286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23055684566497803},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06961256265640259},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06766322255134583}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7937495112419128},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7212710380554199},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7137643098831177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6713021993637085},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.591865599155426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5584880709648132},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.4520570635795593},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4498519003391266},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.43056678771972656},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34082257747650146},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2315465211868286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23055684566497803},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06961256265640259},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06766322255134583},{"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/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<253::aid-nla124>3.0.co;2-b","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":29,"referenced_works":["https://openalex.org/W652672417","https://openalex.org/W1500921805","https://openalex.org/W1608119595","https://openalex.org/W1849833029","https://openalex.org/W1971279003","https://openalex.org/W1982108777","https://openalex.org/W1988914905","https://openalex.org/W1989154489","https://openalex.org/W1993629555","https://openalex.org/W2008815428","https://openalex.org/W2033031224","https://openalex.org/W2034727050","https://openalex.org/W2035463604","https://openalex.org/W2036869265","https://openalex.org/W2038257553","https://openalex.org/W2039643981","https://openalex.org/W2068639060","https://openalex.org/W2069258770","https://openalex.org/W2085207070","https://openalex.org/W2098144997","https://openalex.org/W2104279066","https://openalex.org/W2117625969","https://openalex.org/W2152471993","https://openalex.org/W2320967943","https://openalex.org/W2569133694","https://openalex.org/W6621743430","https://openalex.org/W6636061622","https://openalex.org/W6702708449","https://openalex.org/W6796622633"],"related_works":["https://openalex.org/W1650308825","https://openalex.org/W2482464444","https://openalex.org/W2030139600","https://openalex.org/W4249743596","https://openalex.org/W4362503337","https://openalex.org/W2027272923","https://openalex.org/W4234980991","https://openalex.org/W191482792","https://openalex.org/W4242489673","https://openalex.org/W4235593302"],"abstract_inverted_index":{"An":[0],"aggregation/disaggregation":[1],"iterative":[2],"algorithm":[3],"for":[4],"computing":[5],"stationary":[6],"probability":[7],"vectors":[8],"of":[9,36,73,99],"stochastic":[10],"matrices":[11],"is":[12,21,38,47,91],"analysed.":[13],"Two":[14],"convergence":[15,26,46,62],"results":[16,98],"are":[17,64,103],"presented.":[18,104],"First,":[19],"it":[20],"shown":[22,48],"that":[23,31],"fast,":[24],"global":[25],"can":[27],"be":[28],"achieved":[29],"provided":[30],"a":[32,78],"sufficiently":[33],"high":[34],"number":[35],"relaxations":[37],"performed":[39,56],"on":[40,57,70,83,87],"the":[41,58,71,81,84,88,95,97],"fine":[42,59,85],"level.":[43,60],"Second,":[44],"local":[45],"to":[49],"take":[50],"place":[51],"with":[52],"just":[53],"one":[54],"relaxation":[55],"The":[61],"proofs":[63],"general":[65],"and":[66,86],"require":[67],"no":[68],"assumptions":[69],"magnitude":[72],"off-diagonal":[74],"elements":[75],"(blocks).":[76],"Furthermore,":[77],"relationship":[79],"between":[80],"errors":[82],"coarse":[89],"level":[90],"described.":[92],"To":[93],"illustrate":[94],"theory,":[96],"some":[100],"numerical":[101],"experiments":[102],"\u00a9":[105],"1998":[106],"John":[107],"Wiley":[108],"&":[109],"Sons,":[110],"Ltd.":[111]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
