A homotopy method for solving multilinear systems with M-tensors
It provides a new solution method for a class of multilinear systems arising in applications like PDEs and data mining.
This paper proposes a homotopy method for solving multilinear systems with nonsingular M-tensors and positive right-hand sides, proving convergence and demonstrating effectiveness through numerical experiments.
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector. We analyze the method and prove its convergence to the desired solution. We report some numerical results based on an implementation of the proposed method using a prediction-correction approach for path following.