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Teoriya Veroyatnostei i ee Primeneniya, 1960, Volume 5, Issue 3, Pages 361–366 (Mi tvp4843)  
Short Communications

On the Solution of Peierl’s Integral Equation by the Monte Carlo Method

I. M. Sobol'

Moscow
Full-text PDF (648 kB) Citations (1)
Abstract: The random walks used in [1] to evaluate the least eigenvalue of an integral equation can be used at the same time for computing the first eigenfunction.
In the case of an infinite cylindrical region equation (1) is transformed into (2). The computation of the kernel (3) is performed simultaneously with iterations. A numerical example shows that in general the variance does not decrease when the initial function is improved.
Received: 12.03.1959
English version:
Theory of Probability and its Applications, 1960, Volume 5, Issue 3, Pages 326–331
DOI: https://doi.org/10.1137/1105033
Document Type: Article
Language: Russian
Citation: I. M. Sobol', “On the Solution of Peierl’s Integral Equation by the Monte Carlo Method”, Teor. Veroyatnost. i Primenen., 5:3 (1960), 361–366; Theory Probab. Appl., 5:3 (1960), 326–331
Citation in format AMSBIB
\Bibitem{Sob60}
\by I.~M.~Sobol'
\paper On the Solution of Peierl’s Integral Equation by the Monte Carlo Method
\jour Teor. Veroyatnost. i Primenen.
\yr 1960
\vol 5
\issue 3
\pages 361--366
\mathnet{http://mi.mathnet.ru/tvp4843}
\transl
\jour Theory Probab. Appl.
\yr 1960
\vol 5
\issue 3
\pages 326--331
\crossref{https://doi.org/10.1137/1105033}
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    		Òåîðèÿ âåðîÿòíîñòåé è åå ïðèìåíåíèÿ Theory of Probability and its Applications
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