Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation
We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by $A(c)=[cP+(1-c)E]^T$, where $P$ is a row stochastic matrix, $E$ is a row stochastic rank one matr...
We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by $A(c)=[cP+(1-c)E]^T$, where $P$ is a row stochastic matrix, $E$ is a row stochastic rank one matr...
Some Fast Algorithms for Sequentially Semiseparable Representations
An extended sequentially semiseparable (SSS) representation derived from time-varying system theory is used to capture, on the one hand, the low-rank of the off-diagonal blocks of a matrix for the pu...
An extended sequentially semiseparable (SSS) representation derived from time-varying system theory is used to capture, on the one hand, the low-rank of the off-diagonal blocks of a matrix for the pu...
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Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM. J. Matrix Anal. & Appl. Volume 27, Issue 2, pp. 313-340 (2005)
Issue Date: 2005
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We consider ways of implementing preordering and scaling for symmetric systems and show the effect of using this technique with a multifrontal code for sparse symmetric indefinite systems. After having presented a new method for scaling, we propose a way of using an approximation to a symmetric weighted matching to predefine $1 \times 1$ and $2 \times 2$ pivots prior to the ordering and analysis phase. We also present new classes of orderings called "(relaxed) constrained orderings" that mix structural and numerical criteria.
©2005 Society for Industrial and Applied Mathematics| Permalink: | http://dx.doi.org/10.1137/04061043X |
KEYWORDS and AMS
05C70, 65F05, 65F35, 65F50
PUBLICATION DATA
0895-4798 (print)
1095-7162 (online)
SIAM