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Address: Dr. Venera Khoromskaia Max-Planck-Institute for Mathematics in the Sciences Inselstr., 22-26, D-04103, Leipzig, Germany Tel.: ++49 341-99 59 725 e-mail: vekh [at] mis.mpg.de

Reduced higher order singular value decomposition (RHOSVD) as part of the canonical-to-Tucker (C2T) tensor transform (2006-2007).

Calculation of multi-dimensional (convolution) integrals in 1D complexity (2006-2010)

Tensor-based solver(s) for the Hartree-Fock equation (2009-2013).

Calculation of the 4D two-electron integrals (TEI) tensor in a form of low-rank Cholesky factorization by "1D density fitting" (2012).

Superfast tensor-based summation of long-range electrostatic potentials on finite 3D lattices (2013-2015)

Tensor-based Hartree-Fock solver for finite lattices (at work).

Bethe-Salpeter excitation energies using low-rank tensor factorizations.

Fast computation of the density of states for optical spectra of molecules.

Range-separated tensor format for numerical modeling of multiparticle systems of general type. (2016-2017)

I received University Diploma in Physics in 1974, and next 21 years I have been working at the Joint Institute for Nuclear Research (JINR) in Dubna near Moscow, which at that time had close collaboration with CERN in Geneva. I took part in processing of large scale data from experiments on particles accelerators in high energy physics.

In 2006 I started working at the Max-Planck Institute for Mathematics in the Sciences on Tucker tensor decomposition for function related tensors (together with Boris Khoromskij). This application revealed a number of properties of the Tucker tensor format which were not known before. It showed that for multidimensional tensors obtained by discretization of some classes of multivariate functions on Cartesian grids, the error of the Tucker tensor approximation decays exponentially in the Tucker rank.

On the basis of this knowledge we developed the canonical-to-Tucker decomposition (C2T, 2007) and the reduced higher order singular value decomposition (RHOSVD), which promoted the tensor formats ``avoiding the curse of dimensionality'' (since RHOSVD does not need the construction of a full size tensor). In 2006-2008 we have shown that when using the rank-structured tensor representation for functions and operators, calculation of the 3D convolution integrals with the Newton kernel is reduced to a sequence of one-dimensional operations. [22-27].

In this way, in 2007 the development of the tensor-structured numerical methods was started by solving some problems of 3D grid based ``ab initio`` electronic structure calculations. One of the advantages of this approach for the Hartree-Fock equation is that there is no obligation to usage of the Gaussian-type basis functions, since the analytical integration is completely avoided. We have developed two 3D grid-based Hartree-Fock solvers by tensor numerical methods.

These and other interesting topics (with examples in MATLAB) are discussed in a recent book:

Venera Khoromskaia and Boris N. Khoromskij

Research monograph, De Gruyter, Berlin, 2018.

See also:

Boris N. Khoromskij

Research monograph, De Gruyter, Berlin, 2018.

Radon Series on Computational and Applied Mathematics 19.

last modified 15.08.2018 by V.Khoromskaia