Geodesic
Monte–Carlo estimations for powers of Green operator and the first eigenvalue for Dirichlet boundary value problem
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 125 (2011) no. 4, pp. 82-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we examine the algorithm for computing the powers of a Green operator and the first eigenvalue for the Dirichlet boundary value problem using Monte–Carlo method. The efficiency of numerical realization of these algorithms is also discussed.
Keywords: Monte-Carlo method, eigenvalues of the Dirichlet boundary value problem, Green function, Green operator, distributed computing. 
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     title = {Monte{\textendash}Carlo estimations for powers of {Green} operator and the first eigenvalue for {Dirichlet} boundary value problem},
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A. N. Kuznetsov; I. A. Rytenkova; A. S. Sipin. Monte–Carlo estimations for powers of Green operator and the first eigenvalue for Dirichlet boundary value problem. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 125 (2011) no. 4, pp. 82-92. http://geodesic.mathdoc.fr/item/VSGTU_2011_125_4_a10/

[1] Vladimirov V. S., The equations of mathematical physics, Nauka, Moscow, 1967, 436 pp. | MR

[2] Ermakov S. M., Nekrutkin V. V., Sipin A. S., Random processes for solving classical equations of mathematical physics, Nauka, Moscow, 1984, 206 pp. | MR | Zbl

[3] Mikhaylov G. A., Makarov R. N., “Parametric differentiation and estimation of eigenvalues by the Monte Carlo method”, Siberian Mathematical Journal, 39:4 (1998), 806–815 | DOI | MR

[4] Kuznetsov A. N., Sipin A. S., “Statistical estimates for the degrees of Green operator”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2009, no. 2(19), 114–123 | DOI

[5] Mikhaylov G. A., Marchenko M. A., Parallel realization of statistical simulation and random number generators, Preprint of RAS; Siberian Branch; Institute of Computational Mathematics and Mathematical Geophysics; No. 1154, Novosibirsk, 2001, 20 pp.

[6] Kahan, W., “Pracniques: further remarks on reducing truncation errors”, CACM, 8:1 (1965), 40 | DOI