On the best rank-1 approximation to higher-order symmetric tensors

In this paper, we consider the best rank-1 approximation to higher-order symmetric tensors in the least-squares sense, and show that the best rank-1 approximation of a symmetric tensor with even order mm can be determined by m/2m/2 unit spheres and a best symmetric rank-1 approximation of a symmetric tensor with order 4 and dimension 2 is also its best rank-1 approximation.