Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem

DOI10.1016/j.cam.2007.05.015zbMath1148.15007OpenAlexW1964947065MaRDI QIDQ929938

Gang Wu

Publication date: 19 June 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.05.015

zbMATH Keywords

eigenvaluesJordan canonical formPageRankGoogle matrixgeneralized Google matrixsuccessively rank-one updated matrix

Mathematics Subject Classification ID

Searching and sorting (68P10) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21)

Related Items

The number of distinct eigenvalues of a regular pencil and of a square matrix after rank perturbation ⋮ The eigenvalue shift technique and its eigenstructure analysis of a matrix ⋮ Refined bounds on the number of distinct eigenvalues of a matrix after low-rank update ⋮ On the eigenvalues of a specially updated complex matrix ⋮ On the eigenvalues of specially low-rank perturbed matrices ⋮ On structure-oriented hybrid two-stage iteration methods for the large and sparse blocked system of linear equations ⋮ An Arnoldi-extrapolation algorithm for computing pagerank ⋮ Relationship between the characteristic polynomial and the spectrum of a diagonalizable matrix and those of its low-rank update ⋮ On computing PageRank via lumping the Google matrix

Cites Work

• The eigenvalue problem of a specially updated matrix
• Google pageranking problem: The model and the analysis
• An Arnoldi-extrapolation algorithm for computing pagerank
• Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices
• Matrix Algorithms
• A General Setting for the Parametric Google Matrix
• Matrix Analysis
• Deeper Inside PageRank
• Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation