Tensor Methods for Solving Symmetric \({\mathcal {M}}\)-tensor Systems

Tensor systems involving tensor-vector products (or polynomial systems) are considered. We solve these tensor systems, especially focusing on symmetric \({\mathcal {M}}\)-tensor systems, by some tensor methods. A new tensor method is proposed based on the rank-1 approximation of the coefficient tensor. Numerical examples show that the tensor methods could be more efficient than the Newton method for some \({\mathcal {M}}\)-tensor systems.