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The covariation matrix of solution of a linear algebraic system by the monte carlo method. / Tovstik, Tatiana M.

Statistics and Simulation - IWS 8, Vienna, Austria, September 2015. ed. / Jurgen Pilz; Viatcheslav B. Melas; Dieter Rasch; Karl Moder. Springer Nature, 2018. p. 71-84 (Springer Proceedings in Mathematics and Statistics; Vol. 231).

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Harvard

Tovstik, TM 2018, The covariation matrix of solution of a linear algebraic system by the monte carlo method. in J Pilz, VB Melas, D Rasch & K Moder (eds), Statistics and Simulation - IWS 8, Vienna, Austria, September 2015. Springer Proceedings in Mathematics and Statistics, vol. 231, Springer Nature, pp. 71-84, 8th International Workshop on Simulation, IWS 2015, Vienna, Austria, 21/09/15. https://doi.org/10.1007/978-3-319-76035-3_5

APA

Tovstik, T. M. (2018). The covariation matrix of solution of a linear algebraic system by the monte carlo method. In J. Pilz, V. B. Melas, D. Rasch, & K. Moder (Eds.), Statistics and Simulation - IWS 8, Vienna, Austria, September 2015 (pp. 71-84). (Springer Proceedings in Mathematics and Statistics; Vol. 231). Springer Nature. https://doi.org/10.1007/978-3-319-76035-3_5

Vancouver

Tovstik TM. The covariation matrix of solution of a linear algebraic system by the monte carlo method. In Pilz J, Melas VB, Rasch D, Moder K, editors, Statistics and Simulation - IWS 8, Vienna, Austria, September 2015. Springer Nature. 2018. p. 71-84. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-76035-3_5

Author

Tovstik, Tatiana M. / The covariation matrix of solution of a linear algebraic system by the monte carlo method. Statistics and Simulation - IWS 8, Vienna, Austria, September 2015. editor / Jurgen Pilz ; Viatcheslav B. Melas ; Dieter Rasch ; Karl Moder. Springer Nature, 2018. pp. 71-84 (Springer Proceedings in Mathematics and Statistics).

BibTeX

@inproceedings{a5e778bef67d4a6fbff3cb0f691ca896,
title = "The covariation matrix of solution of a linear algebraic system by the monte carlo method",
abstract = "A linear algebraic system is solved by the Monte Carlo method generating a vector stochastic series. The expectation of a stochastic series coincides with the Neumann series presenting the solution of a linear algebraic system. An analytical form of the covariation matrix of this series is obtained, and this matrix is used to estimate the exactness of the system solution. The sufficient conditions for the boundedness of the covariation matrix are found. From these conditions, it follows the stochastic stability of the algorithm using the Monte Carlo method. The number of iterations is found, which provides for the given exactness of solution with the large enough probability. The numerical examples for systems of the order 3 and of the order 100 are presented.",
keywords = "Covariation matrix of solution, Linear algebraic system, Monte carlo method",
author = "Tovstik, {Tatiana M.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-319-76035-3_5",
language = "English",
isbn = "9783319760346",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer Nature",
pages = "71--84",
editor = "Jurgen Pilz and Melas, {Viatcheslav B.} and Dieter Rasch and Karl Moder",
booktitle = "Statistics and Simulation - IWS 8, Vienna, Austria, September 2015",
address = "Germany",
note = "8th International Workshop on Simulation, IWS 2015 ; Conference date: 21-09-2015 Through 25-09-2015",

}

RIS

TY - GEN

T1 - The covariation matrix of solution of a linear algebraic system by the monte carlo method

AU - Tovstik, Tatiana M.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A linear algebraic system is solved by the Monte Carlo method generating a vector stochastic series. The expectation of a stochastic series coincides with the Neumann series presenting the solution of a linear algebraic system. An analytical form of the covariation matrix of this series is obtained, and this matrix is used to estimate the exactness of the system solution. The sufficient conditions for the boundedness of the covariation matrix are found. From these conditions, it follows the stochastic stability of the algorithm using the Monte Carlo method. The number of iterations is found, which provides for the given exactness of solution with the large enough probability. The numerical examples for systems of the order 3 and of the order 100 are presented.

AB - A linear algebraic system is solved by the Monte Carlo method generating a vector stochastic series. The expectation of a stochastic series coincides with the Neumann series presenting the solution of a linear algebraic system. An analytical form of the covariation matrix of this series is obtained, and this matrix is used to estimate the exactness of the system solution. The sufficient conditions for the boundedness of the covariation matrix are found. From these conditions, it follows the stochastic stability of the algorithm using the Monte Carlo method. The number of iterations is found, which provides for the given exactness of solution with the large enough probability. The numerical examples for systems of the order 3 and of the order 100 are presented.

KW - Covariation matrix of solution

KW - Linear algebraic system

KW - Monte carlo method

UR - http://www.scopus.com/inward/record.url?scp=85047919153&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-76035-3_5

DO - 10.1007/978-3-319-76035-3_5

M3 - Conference contribution

AN - SCOPUS:85047919153

SN - 9783319760346

T3 - Springer Proceedings in Mathematics and Statistics

SP - 71

EP - 84

BT - Statistics and Simulation - IWS 8, Vienna, Austria, September 2015

A2 - Pilz, Jurgen

A2 - Melas, Viatcheslav B.

A2 - Rasch, Dieter

A2 - Moder, Karl

PB - Springer Nature

T2 - 8th International Workshop on Simulation, IWS 2015

Y2 - 21 September 2015 through 25 September 2015

ER -

ID: 49338222