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In this paper, we describe and analyze a novel tensor approximation method for discretized multidimensional functions and operators in R d , based on the idea of multigrid acceleration. The approach stands on successive reiterations of the orthogonal Tucker tensor approximation on a sequence of nested refined grids. On the one hand, it provides a good… (More)

We present a tensor-structured method to calculate the Møller-Plesset (MP2) correction to the Hartree-Fock energy with reduced computational consumptions. The approach originates from the 3D grid-based low-rank factorization of the two-electron integrals performed by the purely algebraic optimization. The computational scheme benefits from fast multilinear… (More)

In this paper, we describe a novel method for robust and accurate iterative solution of the self-consistent Hartree-Fock equation in R 3 based on the idea of tensor-structured computation of the electron density and the nonlinear Hartree and (nonlocal) exchange operators at all steps of the iterative process. We apply the self-consistent field (SCF)… (More)

d We approximate the d-th order tensors (function of discrete variables) by the short-term sum of rank-1 tensors. Canonical model: using a sum of normalized rank-1 tensors

Tensor-structured factorized calculation of two-electron integrals in a general basis Abstract 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 ten-sor factorizations of the TEI unfolding matrix which decrease the computational demands for the… (More)

The present paper contributes to the construction of a " black-box " 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank,… (More)

The Hartree-Fock eigenvalue problem governed by the 3D integro-differential operator is the basic model in ab initio electronic structure calculations. Several years ago the idea to solve the Hartree-Fock equation by fully 3D grid based numerical approach seemed to be a fantasy, and the tensor-structured methods did not exist. In fact, these methods evolved… (More)

In this paper, the tensor-structured numerical evaluation of the Coulomb and exchange operators in the Hartree-Fock equation is supplemented by the usage of recent quantized-TT (QTT) formats. It leads to O(log n) complexity at computationally extensive stages in the rank-structured calculation with the respective 3D Hartree and exchange potentials… (More)