Numerical analysis, linear and multilinear algebra, matrix and tensor analysis, fast algorithms, tensor product formats, dynamical problems, stochastic models
2011M.Sc. in Applied Mathematics and Physics. Moscow Institute of Physics and Technology. Thesis: Iterative methods with the use of tensor decompositions. Excellent.
2009 B.Sc. in Applied Mathematics and Physics. Moscow Institute of Physics and Technology. Thesis: Algebraic methods of sparse grids. Excellent.
Experience
2014-nowPostdoctoral Researcher. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
2011-2014 PhD student. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
2008-2011 Junior Researcher. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia.
Overloaded linear algebra with matrices and vectors in a tensor format.
Compression of given data into a format by direct (SVD) and sparse (cross) procedures.
A collection of examples with analytical tensor formats (finite difference Laplacian, etc.)
Alternating iterative algorithms for solution of linear systems and eigenvalue problems.
tAMEn:http://github.com/dolgov/tamen Purely Matlab routines for alternating iterative solution of the ordinary differential equations
in the tensor train format. See the paper "Alternating minimal energy approach to ODEs and
conservation laws in tensor product formats", [arXiv:1403.8085]. The
main feature of the new algorithm is the spectral accuracy in time and
the possibility to conserve linear invariants and the second norm up to
the machine (not tensor approximation) precision. Another difference with TT-Toolbox is the storage scheme, which allows sparse tensor product factors.
Low-rank cross algorithms for approximations in parametric equations. SIAM conference on Applied Linear Algebra, Atlanta, US, October 28, 2015.
Alternating iteration for low-rank solution of linear systems with large indefinite matrices. 5th Workshop Matrix Equations and Tensor Techniques, University of Bologna, Italy, September 21, 2015.
Low-rank solution of optimization problems constrained by fractional differential equations. Conference European Numerical Mathematics and Advanced Applications, ODTU, Ankara, Turkey, September 14, 2015.
On parallelization of alternating linear schemes for low-rank high-dimensional optimization. Conference Matrix Methods in Mathematics and Applications, Skoltech, Moscow, Russia, August 24, 2015.
Low-rank solution of optimization problems constrained by fractional differential equations. Young Investigators Conference, RWTH, Aachen, Germany, July 22, 2015.
(Poster) Alternating iteration for low-rank solution of high-dimensional equations. Workshop Low-rank Optimization and Applications, HIM, Bonn, Germany, June 9, 2015.