FOM accelerated by an extrapolation method for solving PageRank problems

DOI10.1016/j.cam.2015.09.027zbMath1336.65058OpenAlexW2184151747MaRDI QIDQ898964

Zhao-Li Shen, Ting-Zhu Huang, Chun Wen, Hong-Fan Zhang

Publication date: 21 December 2015

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.2015.09.027

zbMATH Keywords

extrapolationKrylov subspace methodfull orthogonalization methodRitz valuepage rank problem

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Computational methods for sparse matrices (65F50) Searching and sorting (68P10) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical analysis or methods applied to Markov chains (65C40) Eigenvalues, singular values, and eigenvectors (15A18) Iterative numerical methods for linear systems (65F10) Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.) (68U35)

Related Items (12)

Acceleration of the generalized FOM algorithm for computing PageRank ⋮ Off-diagonal low-rank preconditioner for difficult PageRank problems ⋮ A simpler GMRES algorithm accelerated by Chebyshev polynomials for computing PageRank ⋮ An Arnoldi-Inout method accelerated with a two-stage matrix splitting iteration for computing PageRank ⋮ Shifted power-GMRES method accelerated by extrapolation for solving pagerank with multiple damping factors ⋮ An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank ⋮ A variant of the Power-Arnoldi algorithm for computing PageRank ⋮ An adaptive Power-GArnoldi algorithm for computing PageRank ⋮ An efficient elimination strategy for solving PageRank problems ⋮ Multipreconditioned GMRES for simulating stochastic automata networks ⋮ Vector extrapolation based Landweber method for discrete ill-posed problems ⋮ The general inner-outer iteration method based on regular splittings for the PageRank problem

Uses Software

• SparseMatrix

Cites Work

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• The extrapolation-accelerated multilevel aggregation method in PageRank computation
• An Arnoldi-type algorithm for computing Page Rank
• Vector extrapolation methods with applications to solution of large systems of equations and to PageRank computations
• An Arnoldi-extrapolation algorithm for computing pagerank
• On computing PageRank via lumping the Google matrix
• Upper bounds for convergence rates of acceleration methods with initial iterations
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• Expressions and bounds for the GMRES residual
• Extrapolation methods for PageRank computations
• Eigenvalues of rank-one updated matrices with some applications
• Analysis of the convergence of the minimal and the orthogonal residual methods
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• An Inner-Outer Iteration for Computing PageRank
• On the Residual Norm in FOM and GMRES
• GMRES On (Nearly) Singular Systems
• A Power–Arnoldi algorithm for computing PageRank
• The PageRank Vector: Properties, Computation, Approximation, and Acceleration
• Rational extrapolation for the PageRank vector
• Perturbation analysis of singular linear systems with index one^∗
• A Characterization and Representation of the Drazin Inverse
• On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
• Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems
• On adaptively accelerated Arnoldi method for computing PageRank
• Breakdown-free GMRES for Singular Systems
• Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation

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