TY - JOUR

T1 - Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids

AU - Cao, Jian

AU - Genton, Marc G.

AU - Keyes, David E.

AU - Turkiyyah, George M.

N1 - KAUST Repository Item: Exported on 2021-01-14
Acknowledgements: This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST).

PY - 2021/1

Y1 - 2021/1

N2 - 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 -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.

AB - 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 -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.

UR - http://hdl.handle.net/10754/666889

UR - https://linkinghub.elsevier.com/retrieve/pii/S0167947320302565

U2 - 10.1016/j.csda.2020.107165

DO - 10.1016/j.csda.2020.107165

M3 - Article

SN - 0167-9473

SP - 107165

JO - Computational Statistics & Data Analysis

JF - Computational Statistics & Data Analysis

ER -