Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids

Jian Cao, Marc G. Genton, David E. Keyes and George M. Turkiyyah

Computational Statistics & Data Analysis, 2021, vol. 157, issue C

Abstract: The 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 n-dimensional covariance matrix is O(nk2) and the total memory footprint is O(nk), where k 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.

Keywords: Adaptive-cross-approximation; Cholesky factorization; Matérn covariance function; Spatial statistics; Sum of Kronecker products (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302565

DOI: 10.1016/j.csda.2020.107165

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