TY - JOUR
T1 - HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification
AU - Litvinenko, Alexander
AU - Kriemann, Ronald
AU - Genton, Marc G.
AU - Sun, Ying
AU - Keyes, David E.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this publication was supported by funding from the Alexander von Humboldt foundation (chair of Mathematics for Uncertainty Quantification at RWTH Aachen) and Extreme Computing Research Center (ECRC) at King Abdullah University of Science and Technology (KAUST).
PY - 2019/7/12
Y1 - 2019/7/12
N2 - We provide more technical details about the HLIBCov package, which is using parallel hierarchical (H-) matrices to:
• approximates large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement;
•computes matrix-vector product, Cholesky factorization and inverse with a log-linear complexity;
•identify unknown parameters of the covariance function (variance, smoothness, and covariance length);
These unknown parameters are estimated by maximizing the joint Gaussian log-likelihood function. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.
AB - We provide more technical details about the HLIBCov package, which is using parallel hierarchical (H-) matrices to:
• approximates large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement;
•computes matrix-vector product, Cholesky factorization and inverse with a log-linear complexity;
•identify unknown parameters of the covariance function (variance, smoothness, and covariance length);
These unknown parameters are estimated by maximizing the joint Gaussian log-likelihood function. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.
UR - http://hdl.handle.net/10754/626500
UR - https://linkinghub.elsevier.com/retrieve/pii/S2215016119301761
UR - http://www.scopus.com/inward/record.url?scp=85076577156&partnerID=8YFLogxK
U2 - 10.1016/j.mex.2019.07.001
DO - 10.1016/j.mex.2019.07.001
M3 - Article
C2 - 32021810
SN - 2215-0161
VL - 7
SP - 100600
JO - MethodsX
JF - MethodsX
ER -