On perturbations of principal eigenvectors of substochastic matrices
In this report we consider substochastic matrices with some zero rows and study the sensitivity of their eigenvectors to the modifications of zero entries. The analysis is prompted by and directly applied to the Google method of ranking the web sites, which substitutes the pages without outlinks (da...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2016-03, Vol.295, p.149-158 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Bourchtein, Ludmila Bourchtein, Andrei |
| description | In this report we consider substochastic matrices with some zero rows and study the sensitivity of their eigenvectors to the modifications of zero entries. The analysis is prompted by and directly applied to the Google method of ranking the web sites, which substitutes the pages without outlinks (dangling nodes) in the original web link matrix by non-zero rows (dangling vectors). We present an analysis of the influence of artificial links attributed to the dangling nodes on the principal eigenvectors of the web matrix. We clarify when the choice of the dangling vector does not change the original eigenvectors and give an evaluation for perturbations of the principal eigenvectors when they are subject to modification. |
| doi_str_mv | 10.1016/j.cam.2015.01.013 |
| format | Article |
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We clarify when the choice of the dangling vector does not change the original eigenvectors and give an evaluation for perturbations of the principal eigenvectors when they are subject to modification.</description><subject>Dangling nodes</subject><subject>Eigenvectors</subject><subject>Links</subject><subject>Markov chains</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Matrices (mathematics)</subject><subject>Matrix methods</subject><subject>PageRank vector</subject><subject>Perturbation methods</subject><subject>Principal eigenvectors</subject><subject>Substochastic matrices</subject><subject>Vectors (mathematics)</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAUxIMouK5-AG89eml9L22aDZ5k_QsLe9l7SNNUs7RNTdIFv71Z17MwMIc382B-hNwiFAhY3-8LrYaCArICMKk8IwtccZEj56tzsoCS8xwqyi_JVQh7AKgFVgvytB2zyfg4-0ZF68aQuS6bvB21nVSfGfthxoPR0fnfS5ibEJ3-VCFanQ0qeqtNuCYXneqDufnzJdm9PO_Wb_lm-_q-ftzkuhQs5kaUWnS64S3UNYLWVVXrjjHeIWUN7yg1ooaKU1Uy3jCoKRMNxbYECq1i5ZLcnd5O3n3NJkQ52KBN36vRuDnINBWoQKx4iuIpqr0LwZtOpk2D8t8SQR6Byb1MwOQRmARMKlPn4dQxacLBGi-DtmbUprU-EZCts_-0fwBmAHMy</recordid><startdate>20160315</startdate><enddate>20160315</enddate><creator>Bourchtein, Ludmila</creator><creator>Bourchtein, Andrei</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20160315</creationdate><title>On perturbations of principal eigenvectors of substochastic matrices</title><author>Bourchtein, Ludmila ; Bourchtein, Andrei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-e93c9fcb7d06610cc446cf557f125b7f22e960472a357b506259b21d3020da53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Dangling nodes</topic><topic>Eigenvectors</topic><topic>Links</topic><topic>Markov chains</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Matrices (mathematics)</topic><topic>Matrix methods</topic><topic>PageRank vector</topic><topic>Perturbation methods</topic><topic>Principal eigenvectors</topic><topic>Substochastic matrices</topic><topic>Vectors (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bourchtein, Ludmila</creatorcontrib><creatorcontrib>Bourchtein, Andrei</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bourchtein, Ludmila</au><au>Bourchtein, Andrei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On perturbations of principal eigenvectors of substochastic matrices</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2016-03-15</date><risdate>2016</risdate><volume>295</volume><spage>149</spage><epage>158</epage><pages>149-158</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>In this report we consider substochastic matrices with some zero rows and study the sensitivity of their eigenvectors to the modifications of zero entries. 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| ispartof | Journal of computational and applied mathematics, 2016-03, Vol.295, p.149-158 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete - AutoHoldings; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Dangling nodes Eigenvectors Links Markov chains Mathematical analysis Mathematical models Matrices (mathematics) Matrix methods PageRank vector Perturbation methods Principal eigenvectors Substochastic matrices Vectors (mathematics) |
| title | On perturbations of principal eigenvectors of substochastic matrices |
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