Steady-state analysis of google-like stochastic matrices with block iterative methods

Date
2011
Authors
Dayar, T.
Noyan, G. N.
Advisor
Instructor
Source Title
Electronic Transactions on Numerical Analysis
Print ISSN
1068-9613
Electronic ISSN
Publisher
Kent State University
Volume
38
Issue
Pages
69 - 97
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

A Google-like matrix is a positive stochastic matrix given by a convex combination of a sparse, nonnegative matrix and a particular rank one matrix. Google itself uses the steady-state vector of a large matrix of this form to help order web pages in a search engine. We investigate the computation of the steady-state vectors of such matrices using block iterative methods. The block partitionings considered include those based on block triangular form and those having triangular diagonal blocks obtained using cutsets. Numerical results show that block Gauss-Seidel with partitionings based on block triangular form is most often the best approach. However, there are cases in which a block partitioning with triangular diagonal blocks is better, and the Gauss-Seidel method is usually competitive. Copyright © 2011, Kent State University.

Course
Other identifiers
Book Title
Keywords
Block iterative methods, Cutsets, Google, PageRank, Partitionings, Power method, Stochastic matrices, Triangular blocks, Block iterative method, Cutsets
Citation
Published Version (Please cite this version)