Separation of the roots of the systems of nonlinear equations. Stochastic approach
DOI:
https://doi.org/10.21638/spbu01.2023.204Abstract
The work is devoted to the actual problem of separating the roots of nonlinear systems of equations in the case of many variables. The well-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 methods of stochastic optimization. The annealing simulation modeling method and its modification are chosen, which are especially interesting in that they allow efficient implementation on quantum computers. Since quantum ccomputers based on simulated annealing demonstrate quantum superiority, the results obtained can be useful in solving systems of equations on these computing systems.Keywords:
absolute extremum, simulated annealing, systems of equations, root separation, quantum computing
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References
Литература
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References
1. Polak E. Computational methods in optimization: A unified approach. New York, London: Academic Press Publ. (1971) [Rus. ed.: Polak E. Chislennye metody optimizatsii. Edinyi podkhod. Moscow, Mir Publ. (1974).
2. Kirkpatrick S., Gelatt C. D., Vecchi M. Optimization by Simulated annealing. Science 220 (4598), 671-680 (1983).
3. Stella L. Studies of Classical and Quantum Annealing. Ph. D. thesis, SISSA, Trieste (2005). Available at: https://web.archive.org/web/20060516151710/
4. Hastings W. K. Monte Carlo Sampling Methods Using Marcov Chains and Their Applications. Biometrika 57, 97-100 (1970).
5. Metropolis N., Rosenbluth A.W., Rosenbluth M. N., Teller A. H., Teller E. Equations of state calculations by fast computing machines J. Chem. Phys. 21, 1087-1091 (1953).
6. Ermakov S. M., Kulikov D. V., Leora S. N. Towards the analysis of the simulated annealing method in the multiextremal case. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (62), iss. 2, 220-226 (2017). https://doi.org/10.21638/11701/spbu01.2017.205 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 50, iss. 2, 132-137 (2017) https://dx.doi.org/10.3103/S1063454117020042].
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8. Maehler M., Rousseeuw P., Struyf A., Hubert M., Hornik K., Studer M., Roudier P., Gonzalez J., Kozlowski K., Shubert E., Murphy K. Pakage luster (2022). Available at: https://ran.rprojet.org/web/pakages/luster/luster. pdfluster.pdf (accessed: February 21, 2023).
9. Kaufman L., Rousseeuw P. J. Finding groups in data: an introduction to cluster analysis. Wiley (2009).
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Published
2023-05-10
How to Cite
Ermakov, S. M., & Leora, S. N. (2023). Separation of the roots of the systems of nonlinear equations. Stochastic approach. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 226–235. https://doi.org/10.21638/spbu01.2023.204
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
