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

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

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.

Suggested Citation

  • Cao, Jian & Genton, Marc G. & Keyes, David E. & Turkiyyah, George M., 2021. "Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302565
    DOI: 10.1016/j.csda.2020.107165
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    References listed on IDEAS

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    1. Castruccio, Stefano & Genton, Marc G., 2018. "Principles for statistical inference on big spatio-temporal data from climate models," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 92-96.
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    Cited by:

    1. Daniel A. Griffith, 2022. "Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations," Stats, MDPI, vol. 5(4), pages 1-16, November.

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