Результаты поиска по 'vector-matrix description':
Найдено статей: 2
  1. Ryabtsev A.B.
    The error accumulation in the conjugate gradient method for degenerate problem
    Computer Research and Modeling, 2021, v. 13, no. 3, pp. 459-472

    In this paper, we consider the conjugate gradient method for solving the problem of minimizing a quadratic function with additive noise in the gradient. Three concepts of noise were considered: antagonistic noise in the linear term, stochastic noise in the linear term and noise in the quadratic term, as well as combinations of the first and second with the last. It was experimentally obtained that error accumulation is absent for any of the considered concepts, which differs from the folklore opinion that, as in accelerated methods, error accumulation must take place. The paper gives motivation for why the error may not accumulate. The dependence of the solution error both on the magnitude (scale) of the noise and on the size of the solution using the conjugate gradient method was also experimentally investigated. Hypotheses about the dependence of the error in the solution on the noise scale and the size (2-norm) of the solution are proposed and tested for all the concepts considered. It turned out that the error in the solution (by function) linearly depends on the noise scale. The work contains graphs illustrating each individual study, as well as a detailed description of numerical experiments, which includes an account of the methods of noise of both the vector and the matrix.

    Keywords: conjugate gradient method, degenerate problem, noisy oracle.
  2. Minkevich I.G.
    Stoichiometric synthesis of metabolic pathways
    Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1241-1267

    A vector-matrix approach to the theoretical design of metabolic pathways converting chemical compounds, viz., preset substrates, into desirable products is described. It is a mathematical basis for computer–aided generation of alternative biochemical reaction sets executing the given substrate–product conversion. The pathways are retrieved from the used database of biochemical reactions and utilize the reaction stoichiometry and restrictions based on the irreversibility of a part of them. Particular attention is paid to the analysis of restriction interrelations. It is shown that the number of restrictions can be notably reduced due to the existence of families of parallel restricting planes in the space of reaction flows. Coinciding planes of contradirectional restrictions result in the existence of fixed reaction flow values. The problem of exclusion of so called futile cycles is also considered. Utilization of these factors allows essential lowering of the problem complexity and necessary computational resources. An example of alternative biochemical pathway computation for conversion of glucose and glycerol into succinic acid is given. It is found that for a preset “substrate–product” pair many pathways have the same high-energy bond balance.

    Keywords: theoretical biochemistry, substrate, product, conversion, alternative metabolic pathways, stoichiometry, vector-matrix description, irreversible reactions, families of restrictions.
    Views (last year): 6. Citations: 3 (RSCI).

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