Subspace Methods with Local Refinements for Eigenvalue Computation Using Low-Rank Tensor-Train Format

Computing a few eigenpairs from large-scale symmetric eigenvalue problems is far beyond the tractability of classic eigensolvers when the storage of the eigenvectors in the classical way is impossible. We consider a tractable case in which both the coefficient matrix and its eigenvectors can be represented in the low-rank tensor train formats. We propose a subspace optimization method combined with some suitable truncation steps to the given low-rank Tensor Train formats. Its performance can be further improved if the alternating minimization method is used to refine the intermediate solutions locally. Preliminary numerical experiments show that our algorithm is competitive to the state-of-the-art methods on problems arising from the discretization of the stationary Schrodinger equation.NSF [CMMI-1462408, DMS-1115950, DMS-1418724]; NSFC [11322109, 91330202]; National Basic Research Project [2015CB856002]SCI(E)ARTICLE2478-4997