Alternating minimization method for low-rank entrywise approximation of tensors in canonical polyadic format

The approximation of tensors in low-parametric format is an important component in many mathematical modelling and data analysis tasks. One of the most popular low-parametric representations for tensors is the canonical polyadic (CP) decomposition. Nowadays, most of the algorithms for CP approximation aim to construct the approximation in Frobenius norm, however, some applications require entrywise approximation. In this paper, we propose an alternating minimization method to obtain low-rank approximation of tensors in the canonical polyadic format in the Chebyshev norm. Through an extensive evaluation, we demonstrate the effectiveness of the proposed algorithm.