Matrix computations (3rd ed.)
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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
Proceedings of the 13th international conference on World Wide Web
A Reordering for the PageRank Problem
SIAM Journal on Scientific Computing
Google's PageRank and Beyond: The Science of Search Engine Rankings
Google's PageRank and Beyond: The Science of Search Engine Rankings
Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
SIAM Journal on Numerical Analysis
MapReduce: simplified data processing on large clusters
Communications of the ACM - 50th anniversary issue: 1958 - 2008
PageRank Computation, with Special Attention to Dangling Nodes
SIAM Journal on Matrix Analysis and Applications
On computing PageRank via lumping the Google matrix
Journal of Computational and Applied Mathematics
PageRank: Functional dependencies
ACM Transactions on Information Systems (TOIS)
Ordinal Ranking for Google's PageRank
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 Arnoldi-Extrapolation algorithm for computing PageRank
Journal of Computational and Applied Mathematics
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
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In this paper, we introduce five type nodes for lumping the Web matrix, and give a unified presentation of some popular lumping methods for PageRank. We show that the PageRank problem can be reduced to solving the PageRank corresponding to the strongly non-dangling and referenced nodes, and the full PageRank vector can be easily derived by some recursion formulations. Our new lumping strategy can reduce the original PageRank problem to a much smaller one, and it is much cheaper than the recursively reordering scheme. Furthermore, we discuss sensitivity of the PageRank vector, and present a lumping algorithm for computing its first order derivative. Numerical experiments show that the new algorithms are favorable when the matrix is large and the damping factor is high.