Computation of extreme eigenvalues in higher dimensions using block tensor train format
Abstract
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. Applying a block version of the TT format to several vectors simultaneously, we compute the low--lying eigenstates of a system by minimization of a block Rayleigh quotient performed in an alternating fashion for all dimensions. For several numerical examples, we compare the proposed method with the deflation approach when the low--lying eigenstates are computed one-by-one, and also with the variational algorithms used in quantum physics.
Keywords
Cite
@article{arxiv.1306.2269,
title = {Computation of extreme eigenvalues in higher dimensions using block tensor train format},
author = {Sergey V. Dolgov and Boris N. Khoromskij and Ivan V. Oseledets and Dmitry V. Savostyanov},
journal= {arXiv preprint arXiv:1306.2269},
year = {2014}
}
Comments
Submitted to Comput Phys Comm