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arXiv · 1306.2269

Computation of extreme eigenvalues in higher dimensions using block tensor train format

Sergey V. Dolgov·Boris N. Khoromskij·Ivan V. Oseledets·Dmitry V. Savostyanov
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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.

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Sergey V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, Dmitry V. Savostyanov. 2013-06-10. Computation of extreme eigenvalues in higher dimensions using block tensor train format. https://doi.org/10.1016/j.cpc.2013.12.017

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