| Popis: |
For a tensor A we study two closely related problems, the SVD-like tensor decomposition and the approximate tensor diagonalization. We develop two Jacobi-type algorithms, one that maximizes the squares of the diagonal entries of A and the other that maximizes the trace of A. For a general tensor these are the alternating least squares algorithms. The rotation matrices are chosen in each mode one-by-one to maximize the corresponding objective function. We prove the convergence of our algorithms and discuss different initializations, as well as the special case of symmetric tensors. Finally, we present several numerical examples. |
