Computing Tensor $Z$-Eigenvectors with Dynamical Systems

DOI10.1137/18M1229584zbMath1431.15007arXiv1805.00903OpenAlexW2984206738MaRDI QIDQ5203962

Austin R. Benson, David F. Gleich

Publication date: 9 December 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.00903

zbMATH Keywords

numerical integrationeigenvectorslong-term dynamicstensorsspacey random walks

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (7)

Dominant Z-Eigenpairs of Tensor Kronecker Products Decouple ⋮ Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices ⋮ A projection method based on discrete normalized dynamical system for computing C-eigenpairs ⋮ Computing tensor Z-eigenvalues via shifted inverse power method ⋮ Direct methods to compute all \(Z\)-eigenpairs of a tensor with dimension 2 or 3 ⋮ Z-eigenvalue intervals of even-order tensors with application to judge the strong ellipticity of an elasticity tensor ⋮ Three Hypergraph Eigenvector Centralities

Uses Software

• TensorToolbox
• Algorithm 862

Cites Work

• Unnamed Item
• Tensor Decompositions and Applications
• D-eigenvalues of diffusion kurtosis tensors
• Vertex-reinforced random walks and a conjecture of Pemantle
• Real eigenvalues of nonsymmetric tensors
• The number of eigenvalues of a tensor
• Continuous methods for extreme and interior eigenvalue problems
• Eigenvalues of a real supersymmetric tensor
• On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
• Tensor decompositions for learning latent variable models
• Semidefinite Relaxations for Best Rank-1 Tensor Approximations
• A Perron Iteration for the Solution of a Quadratic Vector Equation Arising in Markovian Binary Trees
• Perron-based algorithms for the multilinear PageRank
• Newton Correction Methods for Computing Real Eigenpairs of Symmetric Tensors
• Shifted Power Method for Computing Tensor Eigenpairs
• The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory
• Multilinear PageRank
• Algorithm 862
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• On the solution of a quadratic vector equation arising in Markovian Binary Trees
• Three Hypergraph Eigenvector Centralities
• An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
• All Real Eigenvalues of Symmetric Tensors
• Symmetric Tensors and Symmetric Tensor Rank
• Most Tensor Problems Are NP-Hard
• On the limiting probability distribution of a transition probability tensor
• The Spacey Random Walk: A Stochastic Process for Higher-Order Data

This page was built for publication: Computing Tensor $Z$-Eigenvectors with Dynamical Systems