论文标题
Krylov-schur类似于计算最佳排名的方法 - $（r_1，r_2，r_3）$大和稀疏张量的近似
A Krylov-Schur like method for computing the best rank-$(r_1,r_2,r_3)$ approximation of large and sparse tensors
论文作者
论文摘要
本文涉及计算大型和稀疏张量的最佳低多线性秩近似值的方法。 Krylov型方法已用于此问题；这里引入了块版。为了计算矩阵的部分特征值和奇异值分解，Krylov-schur（重新启动的Arnoldi）方法。我们描述了这种方法对张量的概括，用于计算大型和稀疏张量的最佳低多线性秩近似。与矩阵情况相比，大型张量只能在量量和向量块之间乘以乘以，从而避免了过多的存储器使用情况。事实证明，如果启动近似足够好，则张量Krylov-schur方法是收敛的。给出了用于合成张量和应用的稀疏张量的数值示例，这些张量与高阶正交迭代相比，Krylov-Schur方法的收敛速度更快，更牢固。
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this problem; here block versions are introduced. For the computation of partial eigenvalue and singular value decompositions of matrices the Krylov-Schur (restarted Arnoldi) method is used. We describe a generalization of this method to tensors, for computing the best low multilinear rank approximation of large and sparse tensors. In analogy to the matrix case, the large tensor is only accessed in multiplications between the tensor and blocks of vectors, thus avoiding excessive memory usage. It is proved that, if the starting approximation is good enough, then the tensor Krylov-Schur method is convergent. Numerical examples are given for synthetic tensors and sparse tensors from applications, which demonstrate that for most large problems the Krylov-Schur method converges faster and more robustly than higher order orthogonal iteration.
