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

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.