Computation of extreme eigenvalues in higher dimensions using block tensor train format
摘要：
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.
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关键词：
Theoretical or Mathematical/ eigenvalues and eigenfunctions Hermitian matrices renormalisation tensors/ block tensor train format extreme eigenvalues computation minimal eigenpairs Hermitian matrices tensor train format computational cost feasible low-lying eigenvectors block Rayleigh quotient density matrix renormalization group variational numerical renormalization group DMRG codes/ A0365F Algebraic methods in quantum theory A0210 Algebra, set theory, and graph theory A0220 Group theory
DOI：
10.1016/j.cpc.2013.12.017
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年份：
2014
Elsevier
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掌桥科研
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