Analysis of circulant embedding methods for sampling stationary random fields
A standard problem in uncertainty quantification and in computational statistics is the sampling of stationary Gaussian random fields with given covariance in a d-dimensional (physical) domain. In many applications it is sufficient to perform the sampling on a regular grid on a cube enclosing the ph...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
March 21, 2018
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| In: |
SIAM journal on numerical analysis
Year: 2018, Volume: 56, Issue: 3, Pages: 1871-1895 |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/17M1149730 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1137/17M1149730 Verlag, Volltext: https://epubs.siam.org/doi/abs/10.1137/17M1149730 
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| Author Notes: | I.G. Graham, F.Y. Kuo, D. Nuyens, R. Scheichl, and I.H. Sloan |
| Summary: | A standard problem in uncertainty quantification and in computational statistics is the sampling of stationary Gaussian random fields with given covariance in a d-dimensional (physical) domain. In many applications it is sufficient to perform the sampling on a regular grid on a cube enclosing the physical domain, in which case the corresponding covariance matrix is nested block Toeplitz. After extension to a nested block circulant matrix, this can be diagonalized by FFT - the "circulant embedding method". Provided the circulant matrix is positive definite, this provides a finite expansion of the field in terms of a deterministic basis, with coefficients given by i.i.d. standard normals. In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix is always guaranteed, provided the enclosing cube is sufficiently large. |
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| Item Description: | Gesehen am 19.12.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/17M1149730 |