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On solving systems of linear algebraic equations by Gibbs's method. / Tovstik, T. M.

в: Vestnik St. Petersburg University: Mathematics, Том 44, № 4, 12.2011, стр. 317-323.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Tovstik, TM 2011, 'On solving systems of linear algebraic equations by Gibbs's method', Vestnik St. Petersburg University: Mathematics, Том. 44, № 4, стр. 317-323. https://doi.org/10.3103/S1063454111040133

APA

Tovstik, T. M. (2011). On solving systems of linear algebraic equations by Gibbs's method. Vestnik St. Petersburg University: Mathematics, 44(4), 317-323. https://doi.org/10.3103/S1063454111040133

Vancouver

Tovstik TM. On solving systems of linear algebraic equations by Gibbs's method. Vestnik St. Petersburg University: Mathematics. 2011 Дек.;44(4):317-323. https://doi.org/10.3103/S1063454111040133

Author

Tovstik, T. M. / On solving systems of linear algebraic equations by Gibbs's method. в: Vestnik St. Petersburg University: Mathematics. 2011 ; Том 44, № 4. стр. 317-323.

BibTeX

@article{f508ac8171a744e7829b789c344a4a6b,
title = "On solving systems of linear algebraic equations by Gibbs's method",
abstract = "The paper presents an algorithm of approximate solution of a system of linear algebraic equations by the Monte Carlo method superimposed with ideas of simulating Gibbs and Metropolis fields. A solution in the form of a Neumann series is evaluated, the whole vector of solutions is obtained. The dimension of a system may be quite large. Formulas for evaluating the covariance matrix of a single simulation run are given. The method of solution is conceptually linked to the method put forward in a 2009 paper by Ermakov and Rukavishnikova. Examples of 3 × 3 and 100 × 100 systems are considered to compare the accuracy of approximation for the method proposed, for Ermakov and Rukavishnikova's method and for the classical Monte Carlo method, which consists in consecutive estimation of the components of an unknown vector.",
author = "Tovstik, {T. M.}",
year = "2011",
month = dec,
doi = "10.3103/S1063454111040133",
language = "English",
volume = "44",
pages = "317--323",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - On solving systems of linear algebraic equations by Gibbs's method

AU - Tovstik, T. M.

PY - 2011/12

Y1 - 2011/12

N2 - The paper presents an algorithm of approximate solution of a system of linear algebraic equations by the Monte Carlo method superimposed with ideas of simulating Gibbs and Metropolis fields. A solution in the form of a Neumann series is evaluated, the whole vector of solutions is obtained. The dimension of a system may be quite large. Formulas for evaluating the covariance matrix of a single simulation run are given. The method of solution is conceptually linked to the method put forward in a 2009 paper by Ermakov and Rukavishnikova. Examples of 3 × 3 and 100 × 100 systems are considered to compare the accuracy of approximation for the method proposed, for Ermakov and Rukavishnikova's method and for the classical Monte Carlo method, which consists in consecutive estimation of the components of an unknown vector.

AB - The paper presents an algorithm of approximate solution of a system of linear algebraic equations by the Monte Carlo method superimposed with ideas of simulating Gibbs and Metropolis fields. A solution in the form of a Neumann series is evaluated, the whole vector of solutions is obtained. The dimension of a system may be quite large. Formulas for evaluating the covariance matrix of a single simulation run are given. The method of solution is conceptually linked to the method put forward in a 2009 paper by Ermakov and Rukavishnikova. Examples of 3 × 3 and 100 × 100 systems are considered to compare the accuracy of approximation for the method proposed, for Ermakov and Rukavishnikova's method and for the classical Monte Carlo method, which consists in consecutive estimation of the components of an unknown vector.

UR - http://www.scopus.com/inward/record.url?scp=84859728150&partnerID=8YFLogxK

U2 - 10.3103/S1063454111040133

DO - 10.3103/S1063454111040133

M3 - Article

AN - SCOPUS:84859728150

VL - 44

SP - 317

EP - 323

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 15681197