Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
A Hybrid GMRES algorithm for nonsymmetric linear systems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Extrapolation methods for accelerating PageRank computations
WWW '03 Proceedings of the 12th international conference on World Wide Web
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation
SIAM Journal on Matrix Analysis and Applications
Google's PageRank and Beyond: The Science of Search Engine Rankings
Google's PageRank and Beyond: The Science of Search Engine Rankings
A lock-and-key model for protein--protein interactions
Bioinformatics
Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
SIAM Journal on Numerical Analysis
Comparison of Krylov subspace methods on the PageRank problem
Journal of Computational and Applied Mathematics
PageRank Computation, with Special Attention to Dangling Nodes
SIAM Journal on Matrix Analysis and Applications
Computers & Mathematics with Applications
CONTEST: A Controllable Test Matrix Toolbox for MATLAB
ACM Transactions on Mathematical Software (TOMS)
PageRank: Functional dependencies
ACM Transactions on Information Systems (TOIS)
Arnoldi versus GMRES for computing pageRank: A theoretical contribution to google's pageRank problem
ACM Transactions on Information Systems (TOIS)
Google PageRanking problem: The model and the analysis
Journal of Computational and Applied Mathematics
An Arnoldi-Extrapolation algorithm for computing PageRank
Journal of Computational and Applied Mathematics
An Inner-Outer Iteration for Computing PageRank
SIAM Journal on Scientific Computing
Further Analysis of the Arnoldi Process for Eigenvalue Problems
SIAM Journal on Numerical Analysis
Using search engine technology for protein function prediction
International Journal of Bioinformatics Research and Applications
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PageRank is an algorithm for computing a ranking for every Web page based on the graph of the Web. It plays an important role in Google's search engine. The core of the PageRank algorithm involves computing the principal eigenvector of the Google matrix. Currently, we need to solve PageRank problems with high damping factors, which cost considerable time. A possible approach for accelerating the computation is the Arnoldi-type algorithm. However, this algorithm may not be satisfactory when the damping factor is high and the dimension of the Krylov subspace is low. Even worse, it may stagnate in practice. In this paper, we propose two strategies to improve the efficiency of the Arnoldi-type algorithm. Theoretical analysis shows that the new algorithms can accelerate the original Arnoldi-type algorithm considerably, and circumvent the drawback of stagnation. Numerical experiments illustrate that the accelerated Arnoldi-type algorithms usually outperform many state-of-the-art accelerating algorithms for PageRank. Applications of the new algorithms to function predicting of proteins are also discussed.