We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
59/2013
Computation of extreme eigenvalues in higher dimensions using block tensor train format
Sergey Dolgov, Boris N. Khoromskij, Ivan V. Oseledets and Dmitry Savostyanov
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.
