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

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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.

Original languageEnglish
Title of host publicationStatistics and Simulation - IWS 8, Vienna, Austria, September 2015
EditorsJurgen Pilz, Viatcheslav B. Melas, Dieter Rasch, Karl Moder
PublisherSpringer Nature
Pages71-84
Number of pages14
ISBN (Print)9783319760346
DOIs
StatePublished - 1 Jan 2018
Event8th International Workshop on Simulation, IWS 2015 - Vienna, Austria
Duration: 21 Sep 201525 Sep 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume231
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference8th International Workshop on Simulation, IWS 2015
CountryAustria
CityVienna
Period21/09/1525/09/15

Scopus subject areas

  • Mathematics(all)

Keywords

  • Covariation matrix of solution
  • Linear algebraic system
  • Monte carlo method

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