A preconditioning approach to the pagerank computation problem

Francesco Tudisco, Carmine Di Fiore

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Some spectral properties of the transition matrix of an oriented graph indicate the preconditioning of Euler–Richardson (ER) iterative scheme as a good way to compute efficiently the vertexrank vector associated with such graph. We choose the preconditioner from an algebra U of matrices, thereby obtaining an ERU method, and we observe that ERU can outperform ER in terms of rate of convergence. The proposed preconditioner can be updated at a very low cost whenever the graph changes, as is the case when it represents a generic set of information. The particular U utilized requires a surplus of operations per step and memory allocations, which make ERU superior to ER for not too wide graphs. However, the observed high improvement in convergence rate obtained by preconditioning and the general theory developed, are a reason for investigating different choices of U, more efficient for huge graphs.
Original languageEnglish
Pages (from-to)2222-2246
Number of pages25
JournalLinear Algebra and its Applications
Volume435
Issue number9
Early online date14 May 2011
DOIs
Publication statusPublished - 30 Nov 2011

Keywords

  • pagerank
  • iterative method
  • preconditioning
  • eigenvalues
  • clustering
  • fast discrete transforms

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