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Geostatistical modeling involves many variables and many locations. LU simulation is a popular method for generating realizations, but the covariance matrices that describe the relationships between all of the variables and locations are large and not necessarily amenable to direct decomposition, inversion or manipulation. This paper shows a method similar to LU simulation based on singular value decomposition of large covariance matrices for generating unconditional or conditional realizations using randomized methods. The application of randomized methods in generating realizations, by finding eigenvalues and eigenvectors of large covariance matrices is developed with examples. These methods use random sampling to identify a subspace that captures most of the information in a matrix by considering the dominant eigenvalues. Usually, not all eigenvalues have to be calculated; the fluctuations …