Riemannian Conjugate Gradient Algorithms for Solving λ-Approximation of Stochastic Tensors and Applications

In this paper, we propose an optimal lambda-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.