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Keywords:
Monte Carlo method; integral operators; positive operators
Monte Carlo method; integral operators; positive operators
Summary:
In this paper, a method of numerical solution to the dominant eigenvalue problem for positive integral operators is presented. This method is based on results of the theory of positive operators developed by Krein and Rutman. The problem is solved by Monte Carlo method constructing random variables in such a way that differences between results obtained and the exact ones would be arbitrarily small. Some numerical results are shown.
References:
[1] Krein, M. G., Rutman, M. A.: Linear operators leaving invariant a cone in a Banach space. Usp. Mat. Nauk III, N. 1 (1948), 3–95. (Russian) MR 0027128
[2] Gnedenko, B. V.: The Theory of Probability. Moscow, 1973.
[3] Frank-Kamenietzky, A. O.: Modelling of neutron tracks in reactor calculation by Monte Carlo method. Series “Nuclear reactor physics” 8. Moscow, 1978. (Russian)
[4] Kyncl, J.: The code MOCA. ÚJV Řež, Report ÚJV 6487-R, 1983.
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