低秩Toeplitz张量的高精度随机填充算法

Highaccuracy Randomized Completion Algorithm for the Low Rank Toeplitz Tensor

本文基于高精度填充算法,考虑低秩Toeplitz张量填充问题的求解,通过在每步迭代中将张量随机地按第n模展开并且对它的奇异值分解(SingularValueDecomposition,简记作SVD)进行修正,给出一种具有随机思想的高精度填充算法,并讨论其收敛性.通过对Toeplitz张量及Toeplitz均值张量的数值实验,结果表明新算法比低秩Toeplitz张量的高精度填充算法在计算代价上有明显改进.

In this paper,we consider the solution for the completion problem of low rank Toeplitz tensors,and based on the highaccuracy completion algorithm,present a highaccuracy completion algorithm with randomized technique,in which the nmode tensor is stochastically unfolded and the corresponding singular value decomposition(SVD)is modified in each iteration.Moreover,the convergence of the new algorithm is established.The results of numerical experiments on the Toeplitz tensor and the Toeplitz mean tensor show that the new algorithm is significantly better than the highaccuracy completion algorithm for low rank Toeplitz tensors in terms of computational cost.