The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A(1) (*N) X-1 = C-1, A(1 *)(N )X(2) + A(2) (*N) X-3 = C-2, epsilon(1 *N) X-1 *(M) F-1 + epsilon(1 *N) X-2 *M F-2 + epsilon(2 *N) X-3 *M F-2 = D by using the Moore-Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A (*N) X = C, epsilon( *N) X (* M) F = D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example.