Mathematical Geology

, Volume 19, Issue 2, pp 99–107 | Cite as

Generating large stochastic simulations—The matrix polynomial approximation method

  • Michael W. Davis
Articles
  • 82 Downloads

Abstract

An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement.

Key words

geostatistics simulation Toeplitz matrices block Toeplitz matrices matrix polynomial approximation 

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References

  1. Aho, A. V., Hopcroft, J. E., and Ullman, J. D., 1974. The Design and Analysis of Computer Algorithms: Addison-Wesley, London, p.Google Scholar
  2. Golub, G. H. and Van Loan, C. F., 1985. Matrix Computations: Johns Hopkins, Baltimore, Maryland, p.Google Scholar
  3. Davis, Michael W., 1987. Production of Conditional Simulations via the LU Decomposition of the Covariance Matrix: Math. Geol. v. 19, n. 2, p. 91–98.Google Scholar
  4. Davis, Michael W. and Grivet, Cyril, 1984. Kriging in a Global Neighborhood: Math. Geol., v. 16, no. 3, p. 249–265.Google Scholar
  5. Journel, A. G. and Huijbregts, Ch. J., 1981. Mining Geostatistics: Academic Press, London, 600 p.Google Scholar

Copyright information

© International Association for Mathematical Geology 1987

Authors and Affiliations

  • Michael W. Davis
    • 1
  1. 1.Department of Applied Earth SciencesStanford UniversityStanford

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