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)
The effects of different factors on the embryogenesis and plant regeneration from mature embryos of Russian spring and winter genotypes were studied. Embryogenic callus induction was achieved on MS medium supplemented with different concentrations of 2,4-D (2,4-dichlorophenoxyacetic acid), 2,4,5-T (2,4,5-trichlorophenoxyacetic acid) or Dicamba(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)
The effect of selective agents on the efficiency of Agrobacterium-mediated transformation of pear was shown. The transformation frequency of the pear stock PS no. 217 by a binary vector carrying the nptII gene conferring kanamycin resistance was 0.4 or 3.1%, while the hpt gene for hygromycin resistance used as a selective marker increased transformation(More)
In this paper we accomplish the development of the fast rank–adaptive solver for tensor–structured symmetric positive definite linear systems in higher dimensions. In [9] this problem is approached by alternating minimization of the energy function, which we combine with steps of the basis expansion in accordance with the steepest descent algorithm. In this(More)
Chrysanthemum is one of the most important commercial cut flowers in the world. Early-flowering cultivars are required to produce quality chrysanthemum flowers with a lower cost of production. To shorten the vegetative growth phase of chrysanthemum, three AP1-like genes from Asteraceae were constitutively overexpressed in 80 independent transgenic(More)