  Jacobi-type algorithms for simultaneous approximate diagonalization of real
(or complex) symmetric tensors have been widely used in independent component
analysis (ICA) because of their good performance. One natural way of choosing
the index pairs in Jacobi-type algorithms is the classical cyclic ordering,
while the other way is based on the Riemannian gradient in each iteration. In
this paper, we mainly review in an accessible manner our recent results in a
series of papers about weak and global convergence of these Jacobi-type
algorithms. These results are mainly based on the Lojasiewicz gradient
inequality.
