257 citations · 873 across the 16 of their papers we have counts for
11 papers · 1 filter
Parallel cross interpolation for high-precision calculation of high-dimensional integrals
Sergey Dolgov, Dmitry Savostyanov
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to…
Tensor product approach to quantum control
Diego Quiñones Valles, Sergey Dolgov, Dmitry Savostyanov
In this proof-of-concept paper we show that tensor product approach is efficient for control of large quantum systems, such as Heisenberg spin wires, which are essential for emergi…
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…
Superfast solution of linear convolutional Volterra equations using QTT approximation
Jason A. Roberts, Dmitry V. Savostyanov, Eugene E. Tyrtyshnikov
We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed…
Fast truncation of mode ranks for bilinear tensor operations
Dmitry Savostyanov, Eugene Tyrtyshnikov, Nikolay Zamarashkin
We propose a fast algorithm for mode rank truncation of the result of a bilinear operation on 3-tensors given in the Tucker or canonical form. If the arguments and the result have…
Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case
S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Kryl…