HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification

Abstract
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.

Citation
Litvinenko, A., Kriemann, R., Genton, M. G., Sun, Y., & Keyes, D. E. (2020). HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification. MethodsX, 7, 100600. doi:10.1016/j.mex.2019.07.001

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).

Publisher
Elsevier BV

Journal
MethodsX

DOI
10.1016/j.mex.2019.07.001

arXiv
1709.08625

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S2215016119301761

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