The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The indexable web is more than 11.5 billion pages
WWW '05 Special interest tracks and posters of the 14th international conference on World Wide Web
Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation
SIAM Journal on Matrix Analysis and Applications
The PageRank Vector: Properties, Computation, Approximation, and Acceleration
SIAM Journal on Matrix Analysis and Applications
Arnoldi versus GMRES for computing pageRank: A theoretical contribution to google's pageRank problem
ACM Transactions on Information Systems (TOIS)
An Inner-Outer Iteration for Computing PageRank
SIAM Journal on Scientific Computing
Accelerating the Arnoldi-Type Algorithm for the PageRank Problem and the ProteinRank Problem
Journal of Scientific Computing
| Hi-index | 7.29 |
PageRank algorithm plays a very important role in search engine technology and consists in the computation of the eigenvector corresponding to the eigenvalue one of a matrix whose size is now in the billions. The problem incorporates a parameter @a that determines the difficulty of the problem. In this paper, the effectiveness of stationary and nonstationary methods are compared on some portion of real web matrices for different choices of @a. We see that stationary methods are very reliable and more competitive when the problem is well conditioned, that is for small values of @a. However, for large values of the parameter @a the problem becomes more difficult and methods such as preconditioned BiCGStab or restarted preconditioned GMRES become competitive with stationary methods in terms of Mflops count as well as in number of iterations necessary to reach convergence.