To solve the tensor completion problem,a cyclic algorithm for low rank tensor completion is proposed.Based on the alternating direction multiplier method,the sub-problem is circularly updated,which effectively reduces the cost of tensor expansion,matrix folding and singular value decomposition in the iterative process.At the same time,the convergence analysis of the algorithm is given under reasonable assumptions.Finally,the numerical experiments show that the proposed algorithm is more efficient than other algorithm.

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel ten-sor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel ten-sor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.