Markov chains with memory, tensor formulation, and the dynamics of power iteration

DOI10.1016/j.amc.2017.01.030zbMath1411.60129OpenAlexW2584727969WikidataQ57425961 ScholiaQ57425961MaRDI QIDQ1735395

Moody T. Chu, Sheng-Jhih Wu

Publication date: 28 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2017.01.030

zbMATH Keywords

rate of convergencestationary distributionpower methodtransition probability tensorMarkov chain with memorysecond dominant eigenvalue

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Stochastic matrices (15B51) Markov processes (60J99)

Related Items

Ergodicity Coefficients for Higher-Order Stochastic Processes, On classification of states in higher order Markov chains, Vector Aitken extrapolation method for multilinear PageRank computations, Nonlinear Power-Like and SVD-Like Iterative Schemes with Applications to Entangled Bipartite Rank-1 Approximation, Bayesian framework for simulation of dynamical systems from multidimensional data using recurrent neural network, Nonlinear Power-Like and SVD-Like Iterative Schemes with Applications to Entangled Bipartite Rank-1 Approximation

Uses Software

• ANTELOPE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor
• Eigenvalues and invariants of tensors
• Hidden Markov models in finance
• The number of eigenvalues of a tensor
• Efficient algorithms for computing the largest eigenvalue of a nonnegative tensor
• On the uniqueness and non-uniqueness of the positive \(\mathcal Z\)-eigenvector for transition probability tensors
• The solution methods for the largest eigenvalue (singular value) of nonnegative tensors and convergence analysis
• The spectral theory of tensors and its applications
• A survey on the spectral theory of nonnegative tensors
• Understanding the $QR$ Algorithm
• Multilinear PageRank
• Finding the Largest Eigenvalue of a Nonnegative Tensor
• The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices
• Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor
• ANTELOPE: A Semantic-Aware Data Cube Scheme for Cloud Data Center Networks
• On the limiting probability distribution of a transition probability tensor