A Hessenberg-type algorithm for computing PageRank problems

DOI10.1007/s11075-021-01175-wzbMath1485.65037arXiv1908.00235OpenAlexW3187239659MaRDI QIDQ2118965

Yanyan Li

Publication date: 23 March 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.00235

zbMATH Keywords

Ritz valuesKrylov subspace methodArnoldi processHessenberg processPageRank vector

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Complexity and performance of numerical algorithms (65Y20)

Related Items (3)

An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank ⋮ Distributed PageRank computation with improved round complexities ⋮ Unnamed Item

Uses Software

• CMRH

Cites Work

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• An Arnoldi-Inout algorithm for computing PageRank problems
• A new extrapolation method for PageRank computations
• Accelerating the Arnoldi-type algorithm for the PageRank problem and the ProteinRank problem
• A new look at CMRH and its relation to GMRES
• On certain methods for expanding the characteristic polynomial
• An Arnoldi-type algorithm for computing Page Rank
• A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices
• Google pageranking problem: The model and the analysis
• An Arnoldi-extrapolation algorithm for computing pagerank
• On computing PageRank via lumping the Google matrix
• Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• On a variable smoothing procedure for Krylov subspace methods
• Adaptive methods for the computation of PageRank
• Restarted Hessenberg method for solving shifted nonsymmetric linear systems
• The block Hessenberg process for matrix equations
• The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides
• CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
• Newton generalized Hessenberg method for solving nonlinear systems of equations
• A refined subspace iteration algorithm for large sparse eigenproblems
• Extended and rational Hessenberg methods for the evaluation of matrix functions
• Weighted and flexible versions of block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides
• On global Hessenberg based methods for solving Sylvester matrix equations
• Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides
• Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously
• A new implementation of the CMRH method for solving dense linear systems
• Matrix Krylov subspace methods for linear systems with multiple right-hand sides
• PageRank Beyond the Web
• Eigenvalue Computations Based on IDR
• Numerical Methods for Large Eigenvalue Problems
• An Inner-Outer Iteration for Computing PageRank
• A Power–Arnoldi algorithm for computing PageRank
• The $25,000,000,000 Eigenvector: The Linear Algebra behind Google
• Deeper Inside PageRank
• On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
• A Preconditioned and Shifted GMRES Algorithm for the PageRank Problem with Multiple Damping Factors
• On adaptively accelerated Arnoldi method for computing PageRank
• A Survey of Eigenvector Methods for Web Information Retrieval
• Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
• A Reordering for the PageRank Problem
• Reducing a Matrix to Hessenberg Form
• A Survey on PageRank Computing
• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides

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