Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids
KAUST DepartmentStatistics Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Extreme Computing Research Center
Office of the President
Embargo End Date2023-01-01
Permanent link to this recordhttp://hdl.handle.net/10754/666889
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AbstractThe sum of Kronecker products (SKP) representation for spatial covariance matrices from gridded observations and a corresponding adaptive-cross-approximation-based framework for building the Kronecker factors are investigated. The time cost for constructing an -dimensional covariance matrix is and the total memory footprint is , where is the number of Kronecker factors. The memory footprint under the SKP representation is compared with that under the hierarchical representation and found to be one order of magnitude smaller. A Cholesky factorization algorithm under the SKP representation is proposed and shown to factorize a one-million dimensional covariance matrix in under 600 seconds on a standard scientific workstation. With the computed Cholesky factor, simulations of Gaussian random fields in one million dimensions can be achieved at a low cost for a wide range of spatial covariance functions.
CitationCao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. (2021). Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids. Computational Statistics & Data Analysis, 107165. doi:10.1016/j.csda.2020.107165
SponsorsThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST).