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: • Approximate large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement. • Compute 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.

Keywords

• Parallel
• Hierarchical matrices
• Large datasets
• Matérn covariance
• Random fields
• HLIBCov