{"id":"https://openalex.org/W2166593446","doi":"https://doi.org/10.1137/s0895479804439808","title":"Convergence Analysis of a PageRank Updating Algorithm by Langville and Meyer","display_name":"Convergence Analysis of a PageRank Updating Algorithm by Langville and Meyer","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2166593446","doi":"https://doi.org/10.1137/s0895479804439808","mag":"2166593446"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479804439808","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804439808","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/A5036959652","display_name":"Ilse C. F. Ipsen","orcid":"https://orcid.org/0000-0001-5645-5854"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilse C. F. Ipsen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058163539","display_name":"Steve Kirkland","orcid":"https://orcid.org/0000-0002-9496-5553"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steve Kirkland","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5172,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.96636925,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"4","first_page":"952","last_page":"967"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.948199987411499,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9463000297546387,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pagerank","display_name":"PageRank","score":0.7754726409912109},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6729217767715454},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6478739380836487},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.6311181783676147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6117648482322693},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6066784858703613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4938260018825531},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45291802287101746},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4521026611328125},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.44641929864883423},{"id":"https://openalex.org/keywords/hyperlink","display_name":"Hyperlink","score":0.41407400369644165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41030097007751465},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3760462999343872},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.3615078330039978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32673680782318115},{"id":"https://openalex.org/keywords/web-page","display_name":"Web page","score":0.20662236213684082},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.136211097240448},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08939313888549805}],"concepts":[{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.7754726409912109},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6729217767715454},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6478739380836487},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.6311181783676147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6117648482322693},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6066784858703613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4938260018825531},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45291802287101746},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4521026611328125},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.44641929864883423},{"id":"https://openalex.org/C30088001","wikidata":"https://www.wikidata.org/wiki/Q102014","display_name":"Hyperlink","level":3,"score":0.41407400369644165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41030097007751465},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3760462999343872},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3615078330039978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32673680782318115},{"id":"https://openalex.org/C21959979","wikidata":"https://www.wikidata.org/wiki/Q36774","display_name":"Web page","level":2,"score":0.20662236213684082},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.136211097240448},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08939313888549805},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479804439808","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804439808","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:10.1.1.573.794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.573.794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www4.ncsu.edu/~ipsen/ps/simax43980.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W44158162","https://openalex.org/W156931079","https://openalex.org/W193741420","https://openalex.org/W1490883626","https://openalex.org/W1500921805","https://openalex.org/W1514324734","https://openalex.org/W1520752616","https://openalex.org/W1587314265","https://openalex.org/W1606794504","https://openalex.org/W1670463786","https://openalex.org/W1854214752","https://openalex.org/W1971279003","https://openalex.org/W1995028221","https://openalex.org/W2009561564","https://openalex.org/W2015288352","https://openalex.org/W2036370633","https://openalex.org/W2042624802","https://openalex.org/W2045279300","https://openalex.org/W2054790698","https://openalex.org/W2066636486","https://openalex.org/W2081765494","https://openalex.org/W2082599981","https://openalex.org/W2086036019","https://openalex.org/W2108272874","https://openalex.org/W2161118554","https://openalex.org/W2165469059","https://openalex.org/W2523616508","https://openalex.org/W2569133694","https://openalex.org/W3035235874","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2096221717","https://openalex.org/W4248250357","https://openalex.org/W2054215488","https://openalex.org/W2150410176","https://openalex.org/W2550303287","https://openalex.org/W2542162642","https://openalex.org/W2351647974","https://openalex.org/W2811510744","https://openalex.org/W2075171612","https://openalex.org/W2373471710"],"abstract_inverted_index":{"The":[0,68],"PageRank":[1],"updating":[2],"algorithm":[3],"proposed":[4],"by":[5,43,78,136],"Langville":[6],"and":[7,112],"Meyer":[8],"is":[9,29,41,66,71,99,124],"a":[10,79,86],"special":[11],"case":[12],"of":[13,23,38,51,62,89,94,120,131,141,153,169],"an":[14],"iterative":[15],"aggregation/disaggregation":[16],"(SIAD)":[17],"method":[18,65,70,76,104,123,156],"for":[19],"computing":[20],"stationary":[21],"distributions":[22],"very":[24],"large":[25],"Markov":[26],"chains.":[27],"It":[28,98],"designed,":[30],"in":[31,48,59],"particular,":[32],"to":[33,85,106,158],"speed":[34],"up":[35],"the":[36,44,49,57,63,74,90,95,102,107,116,121,132,138,142,149,154,159,170],"determination":[37],"PageRank,":[39],"which":[40],"used":[42],"search":[45],"engine":[46],"Google":[47,108,160],"ranking":[50],"web":[52,143],"pages.":[53],"In":[54],"this":[55],"paper":[56],"convergence,":[58],"exact":[60],"arithmetic,":[61],"SIAD":[64,69,96,122,155],"analyzed.":[67],"expressed":[72],"as":[73,127,129],"power":[75,103,133,171],"preconditioned":[77],"partial":[80],"LU":[81],"factorization.":[82],"This":[83],"leads":[84],"simple":[87],"derivation":[88],"asymptotic":[91,117,150],"convergence":[92,118,151],"rate":[93,119,152],"method.":[97,134,172],"known":[100],"that":[101,115,130,148,168],"applied":[105,157],"matrix":[109,161],"always":[110],"converges,":[111],"we":[113],"show":[114],"at":[125],"least":[126],"good":[128],"Furthermore,":[135],"exploiting":[137],"hyperlink":[139],"structure":[140],"it":[144],"can":[145,162],"be":[146,163],"shown":[147],"made":[164],"strictly":[165],"faster":[166],"than":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}