HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification
KAUST DepartmentApplied Mathematics and Computational Science
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Preprint Posting Date2017-09-24
Online Publication Date2019-07-12
Print Publication Date2019-07
Permanent link to this recordhttp://hdl.handle.net/10754/626500
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AbstractWe 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.
CitationLitvinenko, 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
SponsorsThe 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).