  In this paper we develop a Jacobi-type algorithm for the approximate
diagonalization of tensors of order $d\geq3$ via tensor trace maximization. For
a general tensor this is an alternating least squares algorithm and the
rotation matrices are chosen in each mode one-by-one to maximize the tensor
trace. On the other hand, for symmetric tensors we discuss a
structure-preserving variant of this algorithm where in each iteration the same
rotation is applied in all modes. We show that both versions of the algorithm
converge to the stationary points of the corresponding objective functions.
