Riemannian Conjugate Gradient Algorithms for Solving λ$$ \boldsymbol{\lambda} $$‐Approximation of Stochastic Tensors and Applications
ABSTRACT In this paper, we propose an optimal ‐approximation model of stochastic tensors arising from higher‐order Markov chains. For exploring a fast solver, we first transform the proposed model into a Riemannian optimization problem equivalently. Then we design two Riemannian optimization algorithms for solving the equivalent problem. Finally, some applications to approximate the solution of higher‐order Markov chains are given. Several numerical examples including the practical data are given to demonstrate the efficiency of the proposed method.
Authors
- Li Wen (ORCID: https://orcid.org/0000-0002-1498-3103)
- Jiao‐fen Li (ORCID: https://orcid.org/0000-0002-7336-2980)
- Seakweng Vong (ORCID: https://orcid.org/0000-0002-3017-3346)
- Dongdong Liu (ORCID: https://orcid.org/0009-0002-6796-2784)
- Yannan Chen (ORCID: https://orcid.org/0000-0002-3121-3602)
Institutions
- Guangdong University of Technology (CN)
- South China Normal University (CN)
- University of Macau (MO)
- Guilin University of Electronic Technology (CN)
Publication Details
- Journal
- Numerical Linear Algebra with Applications
- Published
- 2025-03-20
- DOI
- https://doi.org/10.1002/nla.70010
- Citations
- 2
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 3.07
Funders
- National Natural Science Foundation of China
- Universidade de Macau