Nonsymmetric Algebraic Riccati Equations under the Tensor Product

The nonsymmetric algebraic Riccati equation is proposed by using the tensor product. The existence of its minimal nonnegative solution is studied. The sufficient condition of the existence and the uniqueness of the minimal nonnegative solution is given by M-tensor as well. The solution can be obtained by the fast Fourier transform which save computational cost of computing the required solution. Some numerical experiments are performed.