During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

We resume the recent successes of the grid-based tensor numerical methods and discuss
their prospects in real-space electronic structure calculations. These methods, based on the …

We present a brief survey on the modern tensor numerical methods for multidimensional
stationary and time-dependent partial differential equations (PDEs). The guiding principle of …

We propose Fourier transform algorithms using QTT format for data-sparse approximate
representation of one-and multi-dimensional vectors (m-tensors). Although the Fourier …

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 …

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned
electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation …

This paper deals with the approximation of d d-dimensional tensors, as discrete
representations of arbitrary functions f (x_1, ..., x_d) f (x 1,…, xd) on 0, 1^ d 0, 1 d, in the so …

The Poisson–Boltzmann equation (PBE) is an implicit solvent continuum model for
calculating the electrostatic potential and energies of charged biomolecules in ionic …

In this paper, we introduce the operator dependent range-separated (RS) tensor
approximation of the discretized Dirac delta function (distribution) in R d. It is constructed by …

In this paper, we present a new regularization scheme for the linearized Poisson--Boltzmann
equation (PBE) which models the electrostatic potential of biomolecules in a solvent. This …