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- W2006982184 abstract "Abstract. Random matrices, that is, matrices whose entries are measurable functions of a random vector Z , are encountered in finite element/difference formulations of a broad range of stochastic mechanics problems. Monte Carlo simulation, the only general method for solving this class of problems, is usual impractical when dealing with realistic problems. A new method is proposed for solving this class of problems. The method can be viewed as a smart Monte Carlo simulation. Like Monte Carlo, it calculates statistics for quantities of interest from deterministic matrices corresponding to samples of Z . In contract to Monte Carlo that uses a large number of samples of Z selected at random, the proposed method uses a small number of samples of this vector selected in an optimal manner. The method is based on stochastic reduced models (SROMs) for Z , i.e., random vectors with finite numbers of samples, and surrogate models expressing quantities of interest as known functions of Z . Theoretical arguments are followed by numerical examples providing statistics for inverses of random matrices, solutions of stochastic algebraic equations, and eigenvalues/eigenvectors of random matrices." @default.
- W2006982184 created "2016-06-24" @default.
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- W2006982184 date "2014-04-24" @default.
- W2006982184 modified "2023-09-26" @default.
- W2006982184 title "An efficient Monte Carlo solution for problems with random matrices" @default.
- W2006982184 doi "https://doi.org/10.1515/mcma-2013-0021" @default.
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