Stochastic matrices: ergodicity coefficients and applications to ranking

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dc.contributor.advisor C. D. Meyer, Committee Member en_US
dc.contributor.advisor C. T. Kelley, Committee Member en_US
dc.contributor.advisor S. L. Campbell, Committee Member en_US
dc.contributor.advisor I. C. F. Ipsen, Committee Chair en_US Selee, Teresa Margaret en_US 2010-04-02T18:25:35Z 2010-04-02T18:25:35Z 2008-12-12 en_US
dc.identifier.other etd-11182008-133438 en_US
dc.description.abstract We present two different views of (row) stochastic matrices, which are nonnegative matrices with row sums equal to one. For applications to ranking, we examine the computation of a dominant left eigenvector of a stochastic matrix. The stochastic matrix of interest is called the Google matrix and contains information about how pages of the Internet are linked to one another. The dominant left eigenvector of the Google matrix yields a ranking for each Web page, which helps to determine the order in which search results are returned. These results are presented in Chapter 1. Chapter 2 is concerned with coefficients of ergodicity, which measure the rate at which products of stochastic matrices, especially products whose number of factors is unbounded, converge to a matrix of rank one. Ergodicity arises in the context of Markov chains and signals the tendency of the rows of such products to equalize. We present unified notation and definitions for coefficients of ergodicity applied to stochastic matrices, extend the definitions to general complex matrices, and illustrate the connection between ergodicity coefficients and inclusion regions for eigenvalues and singular values. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject eigenvalues en_US
dc.subject ergodicity coefficient en_US
dc.subject Google en_US
dc.subject PageRank en_US
dc.subject stochastic matrix en_US
dc.title Stochastic matrices: ergodicity coefficients and applications to ranking en_US PhD en_US dissertation en_US Applied Mathematics en_US

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