  In this paper, we propose a Jacobi-type algorithm to solve the low rank
orthogonal approximation problem of symmetric tensors. This algorithm includes
as a special case the well-known Jacobi CoM2 algorithm for the approximate
orthogonal diagonalization problem of symmetric tensors. We first prove the
weak convergence of this algorithm, \textit{i.e.} any accumulation point is a
stationary point. Then we study the global convergence of this algorithm under
a gradient based ordering for a special case: the best rank-2 orthogonal
approximation of 3rd order symmetric tensors, and prove that an accumulation
point is the unique limit point under some conditions. Numerical experiments
are presented to show the efficiency of this algorithm.
