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Activity Number:
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351
- Variable Selection and Computationally Intensive Methods
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
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Sponsor:
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Section on Statistical Computing
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Abstract #313277
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Title:
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Sum of Kronecker Products Representation for Spatial Covariance Matrices and Its Factorization
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Author(s):
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Jian Cao* and Marc Genton and David Keyes and George Turkiyyah
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Companies:
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KAUST and KAUST and King Abdullah University of Science and Technology and American University of Beirut
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Keywords:
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Covariance matrices;
Kronecker products;
Adaptive cross approximation;
Cholesky factorization
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Abstract:
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We introduce a sum of Kronecker products representation for spatial covariance matrices and a corresponding adaptive-cross-approximation based framework for building the Kronecker factors. The time cost for constructing an n-dimensional covariance matrix is O(nk^2) and the total memory footprint is O(nk), where k is the number of Kronecker factors. The memory footprint under this new representation is compared with that under the hierarchical representation and found to be one order of magnitude smaller. A Cholesky factorization algorithm under this representation is proposed and shown to factorize an one-million dimensional covariance matrix within 600 seconds on a normal workstation. With the computed Cholesky factor, simulations of Gaussian random fields in 1M dimensions can be achieved at a low cost for a wide range of spatial covariance functions.
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Authors who are presenting talks have a * after their name.
