A preconditioning approach to the pagerank computation problem

作者：Tudisco Francesco^*; Di Fiore Carmine

来源：Linear Algebra and Its Applications, 2011, 435(9): 2222-2246.

DOI：10.1016/j.laa.2011.04.018

• Pagerank
• Iterative methods
• Preconditioning
• Eigenvalues
• Clustering
• Fast discrete transforms

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 ER(u) method, and we observe that ER(u) 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 ER(u) 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.

• 出版日期2011-11-1