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61. Stochastic Computational Methods and Experiment Design.

Author

Ermakov, S. M. and Melas, V. B.

Abstract

The study presents a brief overview of key results of research conducted at the Statistical Modeling Department of St. Petersburg State University. These results include mathematical substantiation of the computer simulation of randomness, stochastic methods for solving equations, stochastic optimization, and study of the stochastic stability and parallelism of Monte Carlo algorithms. In terms of experiment design, special attention is given to regression experiments with nonlinear parameterization. The references list includes mainly monographs authored by faculty members of the department, with the exception of some articles containing results not included in those. [ABSTRACT FROM AUTHOR]

Published
2023
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62. Separation of Roots of Systems of Nonlinear Equations. Stochastic Approach.

Author

Ermakov, S. M. and Leora, S. N.

Abstract

In this work, we consider the actual problem of separating the roots of nonlinear systems of equations in the case of many variables. The known method of reducing the problem of solving the system to an equivalent extremal problem, which is supposed to be solved by one of the stochastic optimization methods, is used. As the latter, the modeling method of annealing simulation and its modification, which are especially interesting because they allow effective implementation on quantum computers, are chosen. Since quantum computers based on simulated annealing demonstrate quantum superiority, the obtained results can be useful in solving systems of equations on these computers. [ABSTRACT FROM AUTHOR]

Published
2023
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