S. V. Dolgov

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We propose algorithms for the solution of high-dimensional symmetrical positive definite (SPD) linear systems with the matrix and the right-hand side given and the solution sought in a low-rank format. Similarly to density matrix renormalization group (DMRG) algorithms, our methods optimize the components of the tensor product format subsequently. To(More)
Tensors arise naturally in high-dimensional problems in chemistry, financial mathematics and many others. The numerical treatment of such kind of problems is difficult due to the curse of dimensionality: the number of unknowns and computational complexity grows exponentially with the dimension of the problem. To break the curse of dimensionality,(More)
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high–dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. Applying a block version of the TT format to several vectors(More)
We study separability properties of solutions of elliptic equations with piecewise constant coefficients in R d , d ≥ 2. Besides that, we develop efficient tensor-structured preconditioner for the diffusion equation with variable coefficients. It is based only on rank structured decomposition of the tensor of reciprocal coefficient and on the decomposition(More)
The efficiency of immature embryo-derived in vitro culture of G genome wheats is significantly influenced by various auxins and sugars which are used for induction of embryogenic response, and by regeneration media composition for promotion of plant development from subcultured embryogenic calli. The embryogenic calli of Triticum timopheevii has(More)