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- Wolfgang Hackbusch, Boris N. Khoromskij
- Computing
- 2000

The preceding Part I of this paper has introduced a class of matrices (â„‹-matrices) which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The matrices discussedâ€¦ (More)

In the present paper, we discuss the novel concept of super-compressed tensor-structured data formats in high dimensional applications. We describe the multi-folding or quantics based tensorâ€¦ (More)

- Lars Grasedyck, Wolfgang Hackbusch, Boris N. Khoromskij
- Computing
- 2003

In previous papers, a class of hierarchical matrices (â„‹-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate aâ€¦ (More)

- Boris N. Khoromskij, Jens Markus Melenk
- SIAM J. Numerical Analysis
- 2003

In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientificâ€¦ (More)

- S. V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, Dmitry V. Savostyanov
- Computer Physics Communications
- 2014

We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from highâ€“dimensional problems. We use the tensor train format (TT) for vectors andâ€¦ (More)

- Boris N. Khoromskij, Ivan V. Oseledets
- Comput. Meth. in Appl. Math.
- 2010

We investigate the convergence rate of QTT stochastic collocation tensor approximations to solutions of multi-parametric elliptic PDEs, and construct efficient iterative methods for solving arisingâ€¦ (More)

- Venera Khoromskaia, Boris N. Khoromskij, Reinhold Schneider
- SIAM J. Scientific Computing
- 2013

In this paper, the problem of efficient grid-based computation of the two-electron integrals (TEI) in a general basis is considered. We introduce the novel multiple tensor factorizations of the TEIâ€¦ (More)

In this paper we propose two schemes of using the so-called QTTapproximation for the solution of multidimensional parabolic problems. First, we present a simple one-step implicit time integrationâ€¦ (More)

- Vladimir A. Kazeev, Boris N. Khoromskij
- SIAM J. Matrix Analysis Applications
- 2012

We focus on the construction of explicit low-rank representations of matrices in the tensor train (TT) and quantized tensor train (QTT) formats which have been proposed recently for theâ€¦ (More)