Computation of extreme eigenvalues in higher dimensions using block tensor train format
Computation of extreme eigenvalues in higher dimensions using block tensor train format
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DOI：
10.1016/j.cpc.2013.12.017
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发表时间：
2013-06
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影响因子：
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通讯作者：
S. Dolgov;B. Khoromskij;I. Oseledets;D. Savostyanov
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文献类型：
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作者：
S. Dolgov;B. Khoromskij;I. Oseledets;D. Savostyanov
研究了来自高维问题的大厄米矩阵的几个最小特征对的近似计算。我们使用张量序列（TT）格式来克服向量和矩阵的维数诅咒，使存储和计算成本可行。我们在TT格式的块版本中同时近似几个低洼特征向量。计算是通过对所有TT核的块瑞利商依次交替最小化来完成的。该方法结合了密度矩阵重整化群（DMRG）和变分数值重整化群（vNRG）方法的进展。我们将所提出的方法与几种版本的DMRG代码的性能进行了比较，并表明它可能更适合具有大尺寸和/或模态尺寸的系统，或者当需要寻找大量特征态时。
We consider approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high-dimensional problems. We use the tensor train (TT) format for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. We approximate several low-lying eigenvectors simultaneously in the block version of the TT format. The computation is done by the alternating minimization of the block Rayleigh quotient sequentially for all TT cores. The proposed method combines the advances of the density matrix renormalization group (DMRG) and the variational numerical renormalization group (vNRG) methods. We compare the performance of the proposed method with several versions of the DMRG codes, and show that it may be preferable for systems with large dimension and/or mode size, or when a large number of eigenstates is sought.