Paper ID sheet UCL-INMA-2011.011


Jacobi algorithm for the best low multilinear rank approximation of symmetric tensors

Mariya Ishteva, P.-A. Absil, Paul Van Dooren
The problem discussed in this paper is the symmetric best low multilinear rank approximation of third-order symmetric tensors. We propose an algorithm based on Jacobi rotations, for which symmetry is preserved at each iteration. Two numerical examples are provided indicating the need of such algorithms. An important part of the paper consists of proving that our algorithm converges to stationary points of the objective function. This can be considered an advantage of the proposed algorithm over existing symmetry-preserving algorithms in the literature.
Key words
multilinear algebra; higher-order tensor; rank reduction; singular value decomposition; Jacobi rotation
SIAM Journal on Matrix Analysis and Applications, 34(2), pp. 651-672, 2013