257 citations · 873 across the 16 of their papers we have counts for
6 papers · 1 filter
One-site density matrix renormalization group and alternating minimum energy algorithm
Sergey V. Dolgov, Dmitry V. Savostyanov
Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representat…
On the decay of elements of inverse triangular Toeplitz matrix
Neville Ford, D. V. Savostyanov, N. L. Zamarashkin
We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that elements of the inverse matrix, as well as elem…
Quasioptimality of maximum-volume cross interpolation of tensors
Dmitry V. Savostyanov
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal…
Computation of extreme eigenvalues in higher dimensions using block tensor train format
Sergey V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets +1
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…
Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems
Sergey V. Dolgov, Dmitry V. Savostyanov
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6…
Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems
Sergey V. Dolgov, Dmitry V. Savostyanov
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor…